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Understanding Data Measures: A Comprehensive Guide

Learn about different measures of central tendency & dispersion including mean, median, mode, range, variance, and standard deviation. Also explore how to create box and whisker plots to visualize data distribution.

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Understanding Data Measures: A Comprehensive Guide

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  1. 8.3 Describing the Average and Spread of Data Remember to Silence Your Cell Phone and Put It In Your Bag!

  2. Measures of Central Tendency(Averages) • What is an average? • How the data clusters • How the data centers • A typical number • A central number • A representative number

  3. Measures of Central Tendency • Mean • Median • Mode • Midrange

  4. Measures of Central Tendency (cont.) • Arithmetic Mean • The sum of all the data values divided by the number of data values • A balance point • It is affected by extreme values

  5. Measures of Central Tendency (cont.) • Median • The numerical value that is the middle number in an ordered list of the data • If there is an even number of data points, find the mean of the two numbers in the middle of the ordered list • The value about which the data set is equally split

  6. Measures of Central Tendency (cont.) • Mode • The numerical value(s) that occurs most frequently • Bimodal • No mode • Most common data point • Unaffected by all the other scores

  7. Measures of Central Tendency (cont.) • Midrange • The mean of the largest and smallest values in the set of data • The point midway between the largest and smallest numbers in the data set

  8. Measures of Dispersion(Spread or Scattering) • What is a measure of dispersion? • How the data spreads out • How the data is distributed

  9. Measures of Dispersion • Range • Interquartile Range • Variance • Standard Deviation

  10. Measures of Dispersion (cont.) • Range • The difference between the largest and smallest values in the data set

  11. Measures of Dispersion (cont.) • Interquartile range IQR • The range of the middle half of the data • IQR = Q3 – Q1 where Q3 is the third quartile point and Q1 is the first quartile point

  12. To find the IQR • Find the median of the data set. Mark its location and call it Q2. • You now have two subsets of the data. Find the median of the lower subset. Mark its location and call it Q1. • Find the median of the upper subset. Mark its location and call it Q3. • Subtract Q1 from Q3. This value is the IQR.

  13. Measures of Dispersion (cont.) • Variance σ2 • The mean of the squared deviations from the mean of the data set

  14. To Find the Variance • Find the mean,, of the data set • For each number xi in the data set, calculate the deviation of that number from the mean, xi- • Square all the deviation scores obtained in step 2, (xi- )2 • Find the mean of the squared deviations

  15. Measures of Dispersion (cont.) • Standard Deviation σ • The square root of the variance

  16. Box and Whisker Plots • A graphical display of the median, range, and interquartile range • To make a box and whisker plot: • Find the range, median, and IQR of the data • Mark an appropriate scale on either a vertical or horizontal axis • Place points for the lowest score, Q1, Q2, Q3, and the highest score

  17. Draw a box whose top (or right side) is at Q3 and whose bottom (or left side) is at Q1 • Divide the box into two portions with a line segment at Q2 • Draw a line segment from the top of the box (or right side) to the highest score • Draw a line segment from the bottom of the box (or left side) to the lowest score

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