Mean, Median, Mode Social Statistics

This week Mean Median Mode 2

How do we decide which is “best”? The overall goal of central tendency is to find the single score that is most representative for the distribution. 3

Measures of Central Tendency Mean: Arithmetic average sum of scores divided by number of scores most frequently used b/c it uses all scores in the set Median: “Middle” score, when scores are in order corresponds to the 50th percentile appropriate for skewed/open-ended distributions, and distributions with undetermined scores Mode: Most frequently occurring (popular) score appropriate for nominal data 4

Mean 5 (x bar): the mean : sum of the data : number of the data

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 6

Calculate mean LocationNumber of annual customers Lanham Park Store2150 Williamsburg Store1534 Downtown Store The mean or average number of shoppers in each store? Using Excel to do that use your own formula use AVERAGE function

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

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) 9

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? 10

Median in Excel Calculate the median of income level 11

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 12

Calculate mode 185 students: 13 Student distributionNumber or frequency American student150 Asian student30 European student5 Mode = american student

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 14

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” 15

Descriptive Statistics Income Level $135,456 $54,365Mean $37,668Standard Error $34,500Median36084 $32,456Mode#N/A $25,500Standard Deviation Sample Variance Kurtosis Skewness Range Minimum25500 Maximum Sum Count6 16

Exercise 1 (S-p62) Calculate mean, median and mode for the following data: 17 Score1Score2Score

Exercise 2 (S-p62) Writing a sale report to your boss according to the figures of things sold today: 18 specialNumber Soldcost Huge Burger20$2.95 Baby Burger18$1.49 Chicken Littles25$3.50 Porker Burger19$2.95 Yummy Burger17$1.99 Coney Dog20$1.99

Exercise 4 (S-p63) Calculate the average sale 19 toyJuly saleAugust SaleSeptember Sale slammer radar zinger lazertags

Exercise 5 (S-p63) Patient record Mean and median, which is better for what? 20 12/1-12/712/8-12/1512/16-12/ years years years years381219