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Measures of Central Tendencies

Measures of Central Tendencies. Mean, Median, Mode, Range and Box and Whisker Plots. What do these terms mean?. Mean is … …the average. Add all values and divide by the number of values. Median is … …the middle number in a set when ordered least to greatest. Mode is…

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Measures of Central Tendencies

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  1. Measures of Central Tendencies Mean, Median, Mode, Range and Box and Whisker Plots

  2. What do these terms mean? • Mean is … • …the average. Add all values and divide by the number of values. • Median is … • …the middle number in a set when ordered least to greatest. • Mode is… • … the most often occurring number in a set. • Range is … • …a number obtained by subtracting the smallest number of the set from the largest number of the set. • A Box and Whisker Plot … • …displays the median of a set along with a few other key values.

  3. What do these terms mean? • An outlier is… • …a number vastly different from the rest of the data. • The first quartile is… • …the median of the first half of the data. • The third quartile is… • …the median of the second half of the data. • The interquartile range is… • …the third quartile minus the first quartile.

  4. Why do we use them? • Think on your own, then share with a partner why we have these measures of central tendencies. • Class thoughts?

  5. Why do we use them? • Perhaps you said... • To show different kinds of patterns. A mean, for example would be best if you are using data without significant outliers, like average income. But, medians might be more helpful when data is spread out significantly. Mode tells which had the most, so if you are comparing movie box office sales, this make the most sense.

  6. Example 1 • Find the mean, median, mode and range of the set of data below. • 5, 6, 9, 11, 12, 12, 14

  7. Example 1, continued • Mean: 1. Add all the numbers: 5+6+9+11+12+12+14=69 • 2. Divide by 7, since there are 7 numbers in the set. 69/7= The mean is • Median: 1. Put the numbers in order from least to greatest. (In this problem, this is done for you.) • 2. Find the middle number. The median is 11

  8. Example 1, continued • Mode: 1. Find the number occurring most often. The mode is 12. • Range: 1. Subtract the smallest number from the largest number. • 14-5 = 9 The range is 9.

  9. Which number is the outlier? • 3, 4, 5, 3, 124, 7, 2 • The outlier is 124

  10. How many hours a day did you watch TV this summer? • We will create a list on the board. • Then, find the mean, median, mode and range of the data. • Are there any outliers? What are they?

  11. Box and Whisker Plots • Create a box and whisker plot for the data below. • 9, 4, 5, 6, 2, 6, 7, 8, 2, 4, 6, 2, 7, 10, 3

  12. Box and Whisker Plots • Step 1: Arrange the data from smallest to largest. • 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9, 10 • Step 2: Find the median • Median is 6. • Step 3: Find the first and third quartiles • First quartile is 3. Third quartile is 7. • Step 4: Draw the box and whisker plot. • Draw vertical lines on a number line at the minimum, maximum, first and third quartiles and median. Make a box from the first quartile to the third quartile. Draw the “whiskers” from the quartiles to the minimum and maximum. • 2 3 6 7 10

  13. Classwork/Homework • Complete problems Attachment C and E for classwork. (extension/alternate: Attachment G) • Complete problems in Attachment A and I for homework.

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