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Section 12.3 . Analyzing Data. Measures of Central Tendency. Definition 1: The mean , median , and mode are central values that help describe a set of data. They are called measures of central tendency . Example 1. Find the mean, median, and mode for these values

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Section 12 3

Section 12.3

Analyzing Data


Measures of central tendency
Measures of Central Tendency

  • Definition 1: The mean, median, and mode are central values that help describe a set of data. They are called measures of central tendency.


Example 1
Example 1

  • Find the mean, median, and mode for these values

    98, 95, 99, 97, 89, 92, 97, 62, 90


Example 2
Example 2

  • Oceanography Find the mean, median, and the mode of the water temperatures listed for the eastern coast of the Gulf of Mexico.


Box and whisker plots
Box-and-Whisker Plots:

  • Definition 2: If you arrange data in increasing order, then the median divides the data set into two equal parts. You can use the median of each of the parts to divide the set further, into four equal parts. The values separating the four parts are called quartiles.

    5 7 9 10 11 13 14 15 16 17 18 18 20 21 37


Box and whisker plots1
Box-and-Whisker Plots

  • Definition 3: A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.


Example 3
Example 3

  • Make a box-and-whisker plot for these values:

    84, 79, 90, 73, 95, 88, 92, 81, 67


Ticket out the door
Ticket out the Door

  • Find the mean, median, and mode for these values:

    78, 87, 84, 75, 80, 98, 78, 95, 72


Example 4
Example 4

  • Oceanography Using a graphing calculator to find the quartiles of the water temperature data in Example 2. Construct a box-and-whisker plot.


Percentiles
Percentiles

  • Definition 4: A percentile is a number from 0 to 100 that you can associate with x to indicate the percent of the data that are less than or equal to x.


Example 5
Example 5

  • Example 5: Find the values at the 20th and 65th percentiles for the values below.

    21 24 31 45 47 54 61 62 64 65 65 71 82 87 87 93 97 98 98 98


Outlier
Outlier

  • Definition 5: An outlier is an item of data with a value substantially different from the rest of the items in the data set.




Example 6
Example 6

  • Which is an outlier for this set of values? How does the outlier affect each measure of central tendency?

    56 65 73 59 98 65 59


Ticket out the door1
Ticket out the Door

  • Marina has the following quiz grades in her Algebra II class: 84, 90, 96, 100, 67, 88, 90, 92, 94.

    • Find the mean, median, and mode for Marina’s quiz grades.

    • Make a box-and-whisker plot for Marina’s grades.


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