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Mean, Median, Mode

Mean, Median, Mode. Social Statistics. This week. Mean Median Mode. 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. Measures of Central Tendency. Mean: Arithmetic average

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Mean, Median, Mode

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  1. Mean, Median, Mode Social Statistics

  2. This week • Mean • Median • Mode

  3. 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.

  4. 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

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

  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. Calculate mean • The mean or average number of shoppers in each store? • Using Excel to do that • use your own formula • use AVERAGE function

  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 • 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)

  10. 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?

  11. Median in Excel • Calculate the median of income level

  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 • 185 students: Mode = american student

  14. 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

  15. 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”

  16. Descriptive Statistics

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

  18. Exercise 2 (S-p62) • Writing a sale report to your boss according to the figures of things sold today:

  19. Exercise 4 (S-p63) • Calculate the average sale

  20. Exercise 5 (S-p63) • Patient record • Mean and median, which is better for what?

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