1. S519: Evaluation of Information Systems
Social Statistics
Ch2: Mean

2. This week
Mean
Median
Mode

3. What is average
Once the data are collected, next step is how to organize the data
What is the central tendency of your data
Average (group of data can be summarized by average)
Average is the one value that best represents an entire group of scores
Mean
Median
Mode

4. Mean
(x bar): the mean
: sum of the data
: number of the data

5. Calculate mean Lab Location Number of annual customers
Lanham Park Store
2150
Williamsburg Store
1534
Downtown Store
3564
The mean or average number of shoppers in each store?
Using Excel to do that
use your own formula
use AVERAGE function

6. Mean
The sample mean is the measure of central tendency which can approximate the population mean
The mean is very sensitive to extreme scores
It can put the mean in some extreme direction
Make it less representative
Less useful as a measure of central tendency

7. Weighted mean
Lab
See Table9.10 (D-p175)
Do it in Excel

8. Median It is defined as the midpoint in a set of scores
50% of the scores fall above and one half fall below.

9. Calculate median Odd number of data Even number of data Rank them
Median=middle one
Example: 10, 9, 8, 7, 5 (median=8)
Even number of data
Median= sum of two middle data/2
Example: 10, 9, 8, 7, 6, 5 (median=(8+7)/2=7.5)

10. Median in Excel
Lab
Calculate the median of income level

11. Median
The median is insensitive to extreme cases, where the mean is not.
To measure the central tendency:
Have some extreme data, using median
No extreme data, using mean
Example: 14, 3, 2, 1, (mean=5, median=2.5)
Which represents better the central tendency?

12. Mode The mode is the value that occurs most frequently.
Calculate the frequency of all the values in a distribution
The value that occurs most often is the mode

13. Calculate mode 300 students: Lab Student distribution
Number or frequency
American student
150
Asian student 30
European student 5
Mode = american student

14. Summary The mean is the middle point of a set of values,
The median is the middle point of a set of cases
The median cares about how many cases, not the values. So the extreme values don‘t count.

15. When to use what Mean: Median Mode
No extreme scores and are not categorical
Median
Extreme scores and you do not want to distort the average
Mode
Data are categorical in nature and values can only fit into one class
E.g. hair color, political affiliation, religion

16. Descriptive Statistics in Excel
Lab
Take Figure2.9 (S-p57), input these figures to Excel
Data  data analysis  data analysis box  choose Descriptive Statistics  tick “labels in first row”  output range=c1  tick “summary statistics”  click “OK”

17. Descriptive Statistics
Lab
Income Level
$135,456
$54,365
Mean
$37,668
Standard Error
$34,500
Median
36084
$32,456
Mode
#N/A
$25,500
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
109956
Minimum
25500
Maximum
135456
Sum
319945
Count 6

18. Exercise 1 (S-p62)
Lab
Calculate mean, median and mode for the following data:
Score1
Score2
Score3 3 34
154 7 54
167 5 17
132 4 26
145 6 25 14
113 8 24
156 23
123

19. Exercise 2 (S-p62)
Lab
Writing a sale report to your boss according to the figures of things sold today:
special
Number Sold
cost
Huge Burger 20
$2.95
Baby Burger 18
$1.49
Chicken Littles 25
$3.50
Porker Burger 19
Yummy Burger 17
$1.99
Coney Dog

20. Exercise 4 (S-p63) Calculate the average sale Lab toy Julysale
AugustSale
SeptemberSale
slammer
radar zinger
lazertags

21. Exercise 5 (S-p63) Patient record
Lab
Patient record
Mean and median, which is better for what?
12/1-12/7
12/8-12/15
12/16-12/23
0-4 years 12 14 15
5-9 years
10-14 years 24 21
15-19 years 38 19

22. Stat Homework 1 S-p62‐63: 2, 4, 5 Due Jan 28 – week3 How to submit:
Softcopy: Oncourse
Print copy:
write your name, , and S519 in the first page
Submit to me during the class – week 3 (Jan 28)