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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