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Measures of Central Tendency

Measures of Central Tendency . Powerpoint courtesy of aholmes@paulding.k12.ga.us . What is Central Tendency?. In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. What are the 3 measures of Central Tendency?. Mean Median Mode.

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Measures of Central Tendency

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  1. Measures of Central Tendency Powerpoint courtesy of aholmes@paulding.k12.ga.us

  2. What is Central Tendency? In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set.

  3. What are the 3 measures of Central Tendency? • Mean • Median • Mode

  4. MEAN To calculate the mean, we first add together all the scores in a group, and then we divide by the total number of items in the group.

  5. Median • The median is defined as the score corresponding to the 50th percentile. • If scores were ordered from lowest to highest, it would be the score in the middle.

  6. Mode • The mode is the most frequently occurring score • The mode is a better measure of central tendency for dealing with data that involve categories.

  7. What is the first quartile or lower quartile? • first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile

  8. What is the third quartile or upper quartile? • third quartile (designated Q3) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile

  9. Measures of Variability • Range • Interquartile Range • Mean Absolute Deviation

  10. Range • Maximum number minus minimum number. Max # - Min # = RANGE • Tells how spread out the data is.

  11. Interquartile Range • The range within which the middle half (50%) of the results fall. • Upper quartile minus lower quartile • Q3 – Q1

  12. Box-and-Whisker Plots… • A box and whisker plot (sometimes called a boxplot) is a graph that presents information from a five-number summary. • Useful for indicating whether data is skewed (outliers, unusual data) and whether there outliers in the data set. • Box and whisker plots are also very useful when two or more data sets are being compared

  13. Diagram of a Box-and-Whisker Plot

  14. Other Terms to know… • Extremes: The lowest extreme in the set and highest extreme in the set. • Outliers: For a set of numerical data, any value that is markedly smaller or larger than other values. Mathematically, outliers are considered any number that is more than 1.5 times the interquartile range away from the median. For example, in the data set {3, 5, 4, 4, 6, 2, 25, 5, 6, 2} the value of 25 is an outlier. • Basically the one that doesn't belong. Basically, the outlier is the number that stands out.

  15. Mean Absolute Deviation A measure of variability that tells how far or spread out the data is from the mean.

  16. Mean Absolute Deviation… • Average of the absolute values of the difference between each value and the mean. • Large MAD – values more spread out from the mean • Small MAD – values closer to mean and more consistent

  17. How do we find MAD??? • Calculate the mean of the data. • Subtract each data value from the mean. (make the answers positive) • Get the average of the values from step 2. (add and divide by the amount of numbers in the set)

  18. Example: • Consider the data set: 100, 106, 180, 41, 161, 292, 116, 213 • Step 1: Calculate the mean ____________ • Step 2: Rewrite the data set as the difference between the mean • Step 3: Calculate the mean of the new data set __________ (THIS IS THE M.A.D.)

  19. Now you try! • Data Set: 50.8, 51.6, 51.9, 52, 52.5, 52.8, 53.1 • Mean ___________ • M.A.D. _______________

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