Session 3 week 2 central tendency & dispersion
-
Upload
rachel-chung -
Category
Documents
-
view
97 -
download
1
Transcript of Session 3 week 2 central tendency & dispersion
![Page 1: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/1.jpg)
Introduction to Descriptive Statistics Central Tendency
Dispersion
![Page 2: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/2.jpg)
Understand key measures of central tendency • Mean • Median • Mode
Understand key measures of dispersion • Normal Distribution • Skew • Standard Deviation • Z Scores
![Page 3: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/3.jpg)
We often want to know, what’s the typical, more representative value of a variable
Examples: Which gender is more represented in the
sample? Which of our products is the most
popular What is the average selling price? What is the average initial salary?
![Page 4: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/4.jpg)
Mean = the sum of all the members of the list divided by the number of items in the list
Median = the number separating the higher half of a sample from the lower half.
Mode = the most frequent value
![Page 5: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/5.jpg)
A probability distribution that plots all of its values in a symmetrical fashion and most of the results are situated around the probability's mean
![Page 6: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/6.jpg)
![Page 7: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/7.jpg)
Modee
Mediane
Mean
![Page 8: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/8.jpg)
In addition to the most common value, we often want to know how a sample is distributed
Jim’s order was $3. How common is that?
Tia ordered $35. How common is that?
Ed ordered $200. How common is that?
![Page 9: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/9.jpg)
The most common measure of dispersion 1. Calculate the group mean ( ) (average order =$35) 2. Take everyone in the sample (Xi) (Jim ordered $3 Tia ordered $35, & Ed ordered $200, …) 3. Measure how much each one differs from the mean (Xi - ) (Jim’s diff = -$32 Tia’s diff = $0, & Ed’s diff = $165) 4. Square all diff values & add them up (1024+0+27225+……) 5. Divide that total by the sample size (N=310) 6. The result is the standard deviation
![Page 10: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/10.jpg)
The first SD covers the first 34.1% around the mean
Two SDs above & below the mean covers 95% of the distribution
50 percentile 16 percentile 84 percentile
![Page 11: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/11.jpg)
Jim’s order was $3. He’s around -1 SD
Tia ordered $35. She’s an average customer
Ed ordered $200. $200-$35=$165 $165/$32 = 5.15 SD! Ed’s extremely weird!
-1 Standard Deviation $34.72 (mean)-$32 (SD) = $2.72
Mean $34.72 = tip of bell curve
5.15 Standard Deviation $34.72 (mean)+ 5.15 * $32 (SD) = $200
![Page 12: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/12.jpg)
Jim’s order was $3. Jim’s z score is -1
Tia ordered $35. Tia’s z score is 0
Ed ordered $200. $200-$35=$165 $165/$32 = 5.15 SD! Ed’s z score is 5.15
-1 Standard Deviation $34.72 (mean)-$32 (SD) = $2.72
Mean $34.72 = tip of bell curve
5.15 Standard Deviation $34.72 (mean)+ 5.15 * $32 (SD) = $200
![Page 13: Session 3 week 2 central tendency & dispersion](https://reader033.fdocuments.us/reader033/viewer/2022052900/5559d39dd8b42a98208b4cd8/html5/thumbnails/13.jpg)