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
8. 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?
9. 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
10. 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
11. 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
12. 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
