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# Session 3 week 2 central tendency & dispersion-fa2013

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### Session 3 week 2 central tendency & dispersion-fa2013

1. 1. Introduction to Descriptive Statistics Central Tendency Dispersion
2. 2.  Understand key measures of central tendency • Mean • Median • Mode  Understand key measures of dispersion • Normal Distribution • Skew • Standard Deviation • Z Scores
3. 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. 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. 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. 6. Modee Mediane Mean
7. 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. 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. 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. 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. 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