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- 1. Introduction to Descriptive Statistics Central Tendency Dispersion
- 2. Understand key measures of central tendency • Mean • Median • Mode Understand key measures of dispersion • Normal Distribution • Skew • Standard Deviation • Z Scores
- 3. 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?
- 4. 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
- 5. 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
- 6. Modee Mediane Mean
- 7. 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?
- 8. 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.
- 9. The first SD covers the first 34.1% around the mean. Two SDs above & below the mean covers 95% of the distribution. 50th percentile16th percentile 84th percentile
- 10. 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
- 11. 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

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