Find the range and standard deviation of the set of data.?

Find the range and standard deviation of the set of data.

10​, 9​, 7​, 12​, 22

The range is____

The standard deviation is_____

3 Answers

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  • 3 months ago

    The range you should be able to do just by inspection. The range is the difference between the largest and smallest value.

    largest = 22

    smallest = 7

    22 - 7 = 15

    The range is 15.

    To find the standard deviation, first you need to find the mean (the average) of the 5 numbers.

    (10 + 9 + 7 + 12 + 22) / 5

    = 12

    Now take the difference between each number and the mean and square it.

    10 - 12 = -2 --> (-2)² = 4

    9 - 12 = -3 --> (-3)² = 9

    7 - 12 = -5 --> (-5)² = 25

    12 - 12 = 0 --> 0² = 0

    22 - 12 = 10 --> 10² = 100

    Add up all those results and divide by how many numbers you have (5):

    (4 + 9 + 25 + 0 + 100) / 5

    = 138 / 5

    = 27.6

    That's what is known as the *variance*.

    var = 27.6

    To find the standard deviation, you take the square root of the variance.

    σ = √27.6

    σ ≈ 5.25357

    P.S. I'm assuming this is the complete data set and so you want the standard deviation for the *population*.

    There is a slightly different formula if this is the standard deviation of a *sample*. In that case after adding up the squares, you divide by *one less than* how many numbers you have:

    sample variance = 138 / 4 = 34.5

    Then take the square root of that:

    sample s.d. = √34.5 ≈ 5.87367

    But given that this is said to be "the set of data" I'm assuming it is the complete population and the first value (5.25357) is correct.

  • 3 months ago

    Find the range and standard deviation of the set of data.

    10​, 9​, 7​, 12​, 22

    The range is 15

    The standard deviation is 5.8737

  • The range is from 7 to 22

    The standard deviation is 5.87367

    You're supposed to use the formula to solve for Standard Deviation, but I used an online calculator

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