Introduction to Descriptive Statistics Central Tendency

Dispersion

 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 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

 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

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