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# Session 3 week 2 central tendency & dispersion

## by Rachel Chung on Feb 10, 2013

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## Session 3 week 2 central tendency & dispersionPresentation Transcript

• 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 variableExamples: 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 probabilitys 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 16 percentile 50 percentile 84 percentile
• Mean \$34.72 = tip of bell curve 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 5.15 Standard Deviation\$34.72 (mean)-\$32 (SD) = \$2.72 \$34.72 (mean)+ 5.15 * \$32 (SD) = \$200
• Mean \$34.72 = tip of bell curve 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 5.15 Standard Deviation\$34.72 (mean)-\$32 (SD) = \$2.72 \$34.72 (mean)+ 5.15 * \$32 (SD) = \$200