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8.3 Describing the Average and Spread of Data

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

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8.3 Describing the Average and Spread of Data

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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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