Warm-UpSolve for x:

6

51

x

7

87

n n = 6.125

x = -11

Mean, Median, and ModeBy: Christina Carter

Math I

UNIT QUESTION: How do you use probability to make plans and predict for the future?Standard: MM1D1-3

Today’s Question:How do we compare different sets of data?Standard: MM1D3.a.

MeanAlso known as the average.  The mean is found by adding up all of the given data and dividing by the number of data entries.                 Example: the grade 10 math class recently had a mathematics test and the grades were as follows: 78, 66, 82, 89, 75, and 74

78 + 66 + 82 + 89 + 75 + 74 = 464

The mean average of the class is 464 / 6 = 77.3

MeanExample: 1Your parents want you to have at least an 80% test average in this class. So far, you have taken two tests, with scores of 78% and 75%. What must you earn on the third test to average 80%?

x = 87

803

7578

x

MeanExample: 2• 12 of your friends eat a mean of

2.5 cookies.• Another group of 15 of your

friends eat a mean of 3 cookies.• What is the mean number of

cookies all your friends eat?

person

cookies

people

cookies 8.2

1510

3*155.2*10

#

#

MedianThe median is the middle number.  First you arrange the numbers in order from lowest to highest, then you find the middle number by crossing off the numbers until you reach the middle.

Example: Find the median of 5, 9, 3, 7, 12First, put them in order: 3, 5, 7, 9, 12The median is the middle number:

3, 5, 7, 9, 12

MedianWhat if we have an even number of numbers?

Find the median of : 66  74  75  78  82  89

There is no middle number.  What do we do?

Take the two middle numbers and find the average, ( or mean ). 75 + 78 = 153

153 / 2 = 76.5

                             The median is 76.5.

ModeThis is the number that occurs most often.

Example: find the mode of the following data:  

78  56  68  92  84  76  74  56  68  66  78  72  66

65  53  61  62  78  84  61  90  87  77  62  88  81

                                                   The mode is  78.  

RangeThe range of a set of data is the largest number minus the smallest number.

Example: Find the range of 5, 9, 3, 7, 12First, put them in order: 3, 5, 7, 9, 12The range is the largest minus the smallest:

12 – 3 = 9

Best Measure of Central TendencySkew: Data that is not symmetrical when

graphed in a bar chart. Skew is caused by outliers, data that does not

behave nicely. Think of getting around 85% on three tests, and

then getting a 20%. Calculated the mean and median of both data sets:

Data Set A: 85, 85, 85Data Set B: 85, 85, 85, 20Which number would you want to tell you folks?

Data Set Mean Median

A 85 85

B 68.75 85

Best Measure of Central TendencyThe outlier (20%) causes the data to be skewed

left.The outliers will pull the mean more than the

median.We really want to be able to use the mean of the

data if possible. If the data is symmetrical (normal – a word we do not have yet), the best measure of central tendency is the mean.

If the data is skewed, the best measure of central tendency is the median.

Look at Problems 5 – 8 on page 365 asked “Which measure of spread is best to use?”

pg 365 # 5Skewed to the right, so median would be the

best choice for the measure of central tendency.

86 86 87 89 96 100

84 86 88 90 92 94 96 98 100 1020

0.20.40.60.8

1

Series1

pg 365 # 6All the data points are pretty much in the

same area, so the mean would be the best choice of measure of central tendency

32 34 36 38 40 42 440

0.20.40.60.8

1

Series1

pg 365 # 7All the data points are pretty much evenly

spread, so the mean would be the best choice measure of central tendency

50 70 90 110 130 150 1700

0.20.40.60.8

1

Series1

pg 365 # 8Skewed to the right, so median would be the

best choice for the measure of central tendency.

0 50 100 150 200 250 300 3500

0.20.40.60.8

1

Series1

Got it?Cool! Do:“Mean Practice Problems” and pg 365, # 1 – 8 & 16