Tutorial normal v skew distributions
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Transcript of Tutorial normal v skew distributions
![Page 1: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/1.jpg)
Difference between Normal and Skewed Distributions
![Page 2: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/2.jpg)
This presentation will help you determine if the data set from the problem you are asked to solve has a normal or skewed distribution
![Page 3: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/3.jpg)
This presentation will help you determine if the data set from the problem you are asked to solve has a normal or skewed distribution
Normal
Skewed
![Page 4: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/4.jpg)
What is a distribution?
![Page 5: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/5.jpg)
We will illustrate what a distribution is with a data set that describes the hours students’ study
![Page 6: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/6.jpg)
Here is the data set:
![Page 7: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/7.jpg)
Student Hours of Study
![Page 8: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/8.jpg)
Student Hours of Study
Bart 1
![Page 9: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/9.jpg)
Student Hours of Study
Bart 1Basheba 2
![Page 10: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/10.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2
![Page 11: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/11.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3
![Page 12: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/12.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3
![Page 13: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/13.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3
![Page 14: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/14.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4
![Page 15: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/15.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4
![Page 16: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/16.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
![Page 17: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/17.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Data
![Page 18: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/18.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Data Set
![Page 19: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/19.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
From this data set we will create a distribution:
![Page 20: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/20.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
![Page 21: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/21.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
The X Axis, will be the number of hours of
study
![Page 22: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/22.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study
![Page 23: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/23.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1
![Page 24: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/24.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2
![Page 25: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/25.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3
![Page 26: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/26.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4
![Page 27: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/27.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
![Page 28: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/28.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
![Page 29: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/29.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 30: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/30.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 31: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/31.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 32: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/32.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 33: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/33.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 34: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/34.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
The Y Axis, indicates the number of times
the same number occurs
![Page 35: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/35.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Number of Occurrences
![Page 36: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/36.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
![Page 37: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/37.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
![Page 38: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/38.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 39: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/39.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 40: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/40.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 41: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/41.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 42: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/42.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 43: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/43.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 44: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/44.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 45: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/45.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 46: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/46.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 47: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/47.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 48: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/48.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 49: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/49.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 50: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/50.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
![Page 51: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/51.jpg)
Student Hours of Study
Bart 1Basheba 2Bella 2Bob 3Boston 3Bunter 3Buxby 4Bybee 4Bwinda 5
Hours of Study1 2 3 4 5
Num
ber o
f Occ
urre
nces
1
2
3
This is a distribution
![Page 52: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/52.jpg)
One way to represent a distribution like this:
![Page 53: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/53.jpg)
One way to represent a distribution like this:
![Page 54: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/54.jpg)
One way to represent a distribution like this:Is like this:
![Page 55: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/55.jpg)
One way to represent a distribution like this:Is like this:
![Page 56: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/56.jpg)
One way to represent a distribution like this:Is like this:
Normal distributions have the majority of the data in
the middle
![Page 57: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/57.jpg)
One way to represent a distribution like this:Is like this:
Normal distributions have the majority of the data in
the middle
![Page 58: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/58.jpg)
One way to represent a distribution like this:Is like this:
With decreasing but equal amounts
toward the tails
![Page 59: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/59.jpg)
One way to represent a distribution like this:Is like this:
With decreasing but equal amounts
toward the tails
With decreasing but equal amounts
toward the tails
![Page 60: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/60.jpg)
The mean or average works really well with normal distributions
![Page 61: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/61.jpg)
Another way to say it, is that the mean describes well the center point of a normal distribution
![Page 62: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/62.jpg)
![Page 63: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/63.jpg)
A Normal Distribution
![Page 64: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/64.jpg)
The Mean
![Page 65: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/65.jpg)
Here is how you calculate the mean:
![Page 66: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/66.jpg)
![Page 67: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/67.jpg)
Let’s put the data into the distribution
![Page 68: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/68.jpg)
21
2
3
3
3
4
4
5
![Page 69: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/69.jpg)
21
2
3
3
3
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4
5
Mean
![Page 70: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/70.jpg)
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3
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Mean
![Page 71: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/71.jpg)
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Mean
![Page 72: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/72.jpg)
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Mean
![Page 73: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/73.jpg)
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Mean
![Page 74: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/74.jpg)
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Mean
![Page 75: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/75.jpg)
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Mean
![Page 76: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/76.jpg)
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Mean
![Page 77: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/77.jpg)
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Mean
![Page 78: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/78.jpg)
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Mean
![Page 79: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/79.jpg)
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Mean
![Page 80: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/80.jpg)
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Mean
![Page 81: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/81.jpg)
21
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Mean
Divided by the number of total values
![Page 82: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/82.jpg)
21
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Mean
Divided by the number of total values
![Page 83: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/83.jpg)
Mean
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![Page 84: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/84.jpg)
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Mean =
![Page 85: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/85.jpg)
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Mean = = 3
![Page 86: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/86.jpg)
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Mean 3
![Page 87: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/87.jpg)
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Mean 3
![Page 88: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/88.jpg)
The mean is a good estimate of the center of a distribution when the distribution is normal
![Page 89: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/89.jpg)
But, the mean is not a good estimate of the center when the distribution is not normal
![Page 90: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/90.jpg)
This is because of what we call OUTLIERS
![Page 91: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/91.jpg)
What is an outlier?
![Page 92: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/92.jpg)
An outlier is a data point that falls outside the overall pattern of the distribution
![Page 93: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/93.jpg)
As an example, here is the overall pattern
![Page 94: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/94.jpg)
As an example, here is the overall pattern
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5
![Page 95: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/95.jpg)
But what if we changed the 5
![Page 96: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/96.jpg)
But what if we changed the 5
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5
![Page 97: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/97.jpg)
to a 50
![Page 98: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/98.jpg)
to a 50
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50
![Page 99: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/99.jpg)
to a 50
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50
This is an Outlier
![Page 100: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/100.jpg)
To illustrate what happens to the mean when an outlier is present, let’s go back to this distribution:
![Page 101: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/101.jpg)
To illustrate what happens to the mean when an outlier is present, let’s go back to this distribution:
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5
![Page 102: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/102.jpg)
Let’s say one student, instead of studying five hours studies 23 hours a day!!!!!
![Page 103: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/103.jpg)
Watch what happens to the mean:
![Page 104: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/104.jpg)
Before
![Page 105: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/105.jpg)
Mean =
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![Page 106: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/106.jpg)
After
![Page 107: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/107.jpg)
21
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5
![Page 108: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/108.jpg)
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23
![Page 109: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/109.jpg)
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![Page 110: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/110.jpg)
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![Page 111: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/111.jpg)
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Mean =
![Page 112: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/112.jpg)
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Mean =
![Page 113: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/113.jpg)
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Mean =
![Page 114: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/114.jpg)
Once again, BEFORE
![Page 115: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/115.jpg)
Once again, BEFORE
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Mean =
![Page 116: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/116.jpg)
AFTER
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Mean =
![Page 117: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/117.jpg)
Just by changing one value from “5” to “23” the mean changed by two values (from “3” to “5”)
![Page 118: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/118.jpg)
Thus, the mean is very sensitive to outliers
![Page 119: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/119.jpg)
Therefore, the mean is not a good estimate of the center of a distribution when the distribution is NOT NORMAL
![Page 120: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/120.jpg)
Therefore, the mean is not a good estimate of the center of a distribution when the distribution is NOT NORMAL
![Page 121: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/121.jpg)
Therefore, the mean is not a good estimate of the center of a distribution when the distribution is NOT NORMAL
![Page 122: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/122.jpg)
Therefore, the mean is not a good estimate of the center of a distribution when the distribution is NOT NORMAL
![Page 123: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/123.jpg)
So, how do you know if your data is normally distributed?
Go to the Learning Module entitled: Assessing Skew. You will find it next to the link for this presentation.
![Page 124: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/124.jpg)
So, how do you know if your data is normally distributed?
Go to the Learning Module entitled: Assessing Skew. You will find it next to the link for this presentation.
![Page 125: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/125.jpg)
So, how do you know if your data is normally distributed?
Go to the Learning Module entitled: Assessing Skew. You will find it next to the link for this presentation.
After you have viewed that learning module use SPSS to assess the skew of your data.
![Page 126: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/126.jpg)
Is your data normally distributed or skewed?
![Page 127: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/127.jpg)
If your data was skewed with a critical ratio greater than 2.0 or less than -2.0 then select
Skewed
![Page 128: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/128.jpg)
Otherwise select
Normal
![Page 129: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/129.jpg)
When your distribution is normal then it is appropriate to use the mean as a way to know something about the center point of the distribution.
![Page 130: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/130.jpg)
Normal distributions use the mean in their calculations
Skewed distributions use the median
![Page 131: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/131.jpg)
What is the median?
![Page 132: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/132.jpg)
The median is simply the middle score of a data set where
![Page 133: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/133.jpg)
The median is simply the middle score of a data set where • 50% of the scores fall below it and
![Page 134: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/134.jpg)
The median is simply the middle score of a data set where • 50% of the scores fall below it and • 50% of the scores are above it
![Page 135: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/135.jpg)
To illustrate let’s go back to this distribution:
![Page 136: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/136.jpg)
To illustrate let’s go back to this distribution:
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![Page 137: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/137.jpg)
With the Median we simply determine the mid point:
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![Page 138: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/138.jpg)
Median
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![Page 139: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/139.jpg)
Median
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4 units
![Page 140: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/140.jpg)
Median
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4 units 4 units
![Page 141: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/141.jpg)
Median
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4 units 4 units
![Page 142: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/142.jpg)
Median
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4 units 4 units
![Page 143: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/143.jpg)
Median
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4 units 4 units
This is the Median
![Page 144: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/144.jpg)
Notice that the Median is unaffected by outliers
![Page 145: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/145.jpg)
To illustrate this, we’ll change the value “5” to a “10”:
![Page 146: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/146.jpg)
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![Page 147: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/147.jpg)
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![Page 148: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/148.jpg)
Watch what happens to the median:
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![Page 149: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/149.jpg)
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Median 10
![Page 150: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/150.jpg)
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Median 10 4 units
10
![Page 151: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/151.jpg)
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Median 10 4 units
10
4 units
![Page 152: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/152.jpg)
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Median 10 4 units
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4 units
![Page 153: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/153.jpg)
Median
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4 units 4 units
Hmm, it’s still 3
![Page 154: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/154.jpg)
But, what if we change the value 10 to 1,000!!!
![Page 155: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/155.jpg)
Watch again what happens to the median:
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1,000
![Page 156: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/156.jpg)
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Median 1000
1,000
![Page 157: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/157.jpg)
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Median 1000 4 units
1,000
![Page 158: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/158.jpg)
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Median 1000 4 units 4 units
1,000
![Page 159: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/159.jpg)
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Median 1000 4 units 4 units
1,000
![Page 160: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/160.jpg)
Median
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4 units 4 units
1,000
What do you know – It’s still 3
![Page 161: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/161.jpg)
Here is the key take away:
![Page 162: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/162.jpg)
The mean is affected by outliers
![Page 163: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/163.jpg)
The mean is affected by outliers
The median is not affected by outliers
![Page 164: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/164.jpg)
Therefore the mean is used with more or less NORMAL DISTRIBUTIONS
![Page 165: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/165.jpg)
Therefore the mean is used with more or less NORMAL DISTRIBUTIONS
![Page 166: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/166.jpg)
And the median is used with SKEWED OR NON-NORMAL DISTRIBUTIONS
![Page 167: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/167.jpg)
And the median is used with SKEWED OR NON-NORMAL DISTRIBUTIONS
![Page 168: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/168.jpg)
And the median is used with SKEWED OR NON-NORMAL DISTRIBUTIONS
![Page 169: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/169.jpg)
And the median is used with SKEWED OR NON-NORMAL DISTRIBUTIONS
![Page 170: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/170.jpg)
So, based on your analysis, which distribution best reflect your data set:
![Page 171: Tutorial normal v skew distributions](https://reader037.fdocuments.us/reader037/viewer/2022103019/55c7f6a4bb61ebc85b8b45a5/html5/thumbnails/171.jpg)
So, based on your analysis, which distribution best reflect your data set:
Normal
Skewed