S519: Evaluation of Information Systems

Social Statistics

Ch2: Mean

This week

Mean Median Mode

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

Mean

n

XX ___

(x bar): the mean

: sum of the data

: number of the data

___

X

X

n

Calculate mean

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

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

Weighted mean

See Table9.10 (D-p175)

Do it in Excel

Median

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

below.

Calculate median

Odd number of data Rank them Median=middle one Example: 10, 9, 8, 7, 5 (median=8)

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

Median in Excel

Calculate the median of income level

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?

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

Calculate mode

300 students:

Student distribution Number or frequency

American student 150

Asian student 30

European student 5

Mode = american student

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.

When to use what

Mean: 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

Descriptive Statistics in Excel

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”

Descriptive Statistics

Income Level Income Level$135,456

$54,365 Mean 53324.16667$37,668 Standard Error 16887.71824$34,500 Median 36084$32,456 Mode #N/A$25,500 Standard Deviation 41366.2926

Sample Variance 1711170163Kurtosis 4.861219327Skewness 2.173756462Range 109956Minimum 25500Maximum 135456Sum 319945Count 6

Exercise 1 (S-p62)

Calculate mean, median and mode for the following data:

Score1 Score2 Score33 34 1547 54 1675 17 1324 26 1455 34 1546 25 1457 14 1138 24 1566 25 1545 23 123

Exercise 2 (S-p62)

Writing a sale report to your boss according to the figures of things sold today:

special Number Sold costHuge Burger 20 $2.95 Baby Burger 18 $1.49 Chicken Littles 25 $3.50 Porker Burger 19 $2.95 Yummy Burger 17 $1.99 Coney Dog 20 $1.99

Exercise 4 (S-p63)

Calculate the average sale

toy Julysale AugustSale SeptemberSaleslammer 12345.00 14453.00 15435.00radar zinger 31454.00 34567.00 29678.00lazertags 3253.00 3121.00 5131.00

Exercise 5 (S-p63)

Patient record Mean and median, which is better for what?

12/1-12/7 12/8-12/15 12/16-12/230-4 years 12 14 155-9 years 15 12 1410-14 years 12 24 2115-19 years 38 12 19

Stat Homework 1

S-p62‐63: 2, 4, 5 Due Jan 28 – week3 How to submit:

Softcopy: Oncourse Print copy:

write your name, email, and S519 in the first page Submit to me during the class – week 3 (Jan 28)