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24 August, 13:02

The ages of the guests on a museum tour are 32, 14, 18, 29, 65, 50, 48, 44, and 28. Find the five-number summary of the ages.

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  1. 24 August, 13:11
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    Minimum = 14, 1st Q = 23, median = 32, 3rd Q = 49, maximum = 65

    Step-by-step explanation:

    * Lets explain what is the five-number summary

    - The five-number summary for a set of data, are:

    # The minimum

    # First quartile

    # Median

    # Third quartile

    # The maximum

    ∵ The ages of the guests are 32, 14, 18, 29, 65, 50, 48, 44, 28

    # The steps to find them

    1. Put your numbers in ascending order

    ∴ 14, 18, 28, 29, 32, 44, 48, 50, 65

    2. Find the minimum and maximum for your data

    ∴ The minimum is 14

    ∴ The maximum is 65

    3. Find the median where the median is the middle number.

    ∵ There are 9 ages then the middle age is the 5th age

    ∵ The 5th age is 32

    ∴ The median is 32

    4. The first quartile is the median of the lower half of the data

    ∵ The lower half of the ages are 14, 18, 28, 29

    ∵ The numbers of ages are even

    ∴ The first quartile is the average of the two middle ages

    ∴ The 1st quartile = (18 + 28) / 2 = 23

    ∴ The 1st quartile is 23

    5. The third quartile is the median of the upper half of the data

    ∵ The upper half of the ages are 44, 48, 50, 65

    ∵ The numbers of ages are even

    ∴ The third quartile is the average of the two middle ages

    ∴ The 3rd quartile = (48 + 50) / 2 = 49

    ∴ The 3rd quartile is 49

    * The five-number summary of the ages are:

    Minimum = 14, 1st Q = 23, median = 32, 3rd Q = 49, maximum = 65
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