This document introduces key concepts in descriptive statistics including measures of central tendency (mean, median, mode) and dispersion (standard deviation, normal distribution, skew, z-scores). It explains that measures of central tendency describe a typical or representative value for a variable, while measures of dispersion describe how spread out the values are. The document provides examples of calculating and interpreting the mean, standard deviation, and z-scores. It illustrates how statistical values like standard deviation can be used to determine how common or extreme certain observations are relative to the average or mean value.

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

7. Modee
Mediane
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