Session 3 week 2 central tendency & dispersion-fa2013

Introduction to Descriptive Statistics

Central TendencyDispersion

Understand key measures of central tendency• Mean• Median• Mode

Understand key measures of dispersion• Normal Distribution• Skew• Standard Deviation• Z Scores

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?

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

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

Modee

Mediane

Mean

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?

The most common measure of dispersion1. 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.

The first SD covers the first 34.1% around the mean. Two SDs above & below the mean covers 95% of the

distribution.

50th percentile

16th percentile 84th percentile

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

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