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 (x bar): the mean : sum of the data : number of the data

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

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 Lab 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 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)

Median in Excel Lab 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: Lab 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: 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

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”

Descriptive Statistics Lab 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 1711170163 Kurtosis 4.861219327 Skewness 2.173756462 Range 109956 Minimum 25500 Maximum 135456 Sum 319945 Count 6

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

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

Exercise 4 (S-p63) Calculate the average sale Lab toy Julysale AugustSale SeptemberSale slammer 12345.00 14453.00 15435.00 radar zinger 31454.00 34567.00 29678.00 lazertags 3253.00 3121.00 5131.00

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

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)