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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 X ___ X (x bar): the mean X : sum of the data n : number of the data n Lab 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 Lab 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) Lab 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 Lab 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: Median No extreme scores and are not categorical 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 Lab 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” Lab Descriptive Statistics Income Level Income Level $135,456 $54,365 $37,668 $34,500 $32,456 $25,500 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 53324.16667 16887.71824 36084 #N/A 41366.2926 1711170163 4.861219327 2.173756462 109956 25500 135456 319945 6 Lab Exercise 1 (S-p62) Calculate mean, median and mode for the following data: Score1 Score2 3 7 5 4 5 6 7 8 6 5 34 54 17 26 34 25 14 24 25 23 Score3 154 167 132 145 154 145 113 156 154 123 Lab Exercise 2 (S-p62) Writing a sale report to your boss according to the figures of things sold today: special Number Sold Huge Burger Baby Burger Chicken Littles Porker Burger Yummy Burger Coney Dog cost 20 18 25 19 17 20 $2.95 $1.49 $3.50 $2.95 $1.99 $1.99 Lab Exercise 4 (S-p63) Calculate the average sale toy slammer radar zinger lazertags Julysale AugustSale SeptemberSale 12345.00 14453.00 15435.00 31454.00 34567.00 29678.00 3253.00 3121.00 5131.00 Lab Exercise 5 (S-p63) Patient record Mean and median, which is better for what? 12/1-12/7 0-4 years 5-9 years 10-14 years 15-19 years 12 15 12 38 12/8-12/15 12/16-12/23 14 15 12 14 24 21 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)