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

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

160​, 165​, 170​, 175​, 180​, 185​, 190

The range is______

The standard deviation is_______

1 Answer

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  • 4 months ago

    The method is exactly the same as your other question.

    What's the biggest number? 190

    What's the smallest number? 160

    What's the difference? 190 - 160 = 30

    That's the *range*.

    What's the mean (average) of the 7 numbers:

    (160 + 165 + 170 + 175 + 180 + 185 + 190) / 7

    = 175

    Note: Because the numbers go up in a progression of 5 each time, the average will be the same as the middle number. A quick tip if you need to figure this out quickly.

    Now square the difference between each number and this mean:

    160 - 175 = -15 --> (-15)² = 225

    165 - 175 = -10 --> (-10)² = 100

    170 - 175 = -5 --> (-5)² = 25

    etc.

    Assuming this is the complete *population* of data, we add those up and divide by *7*. (I don't see any mention that this is a *sample* of data).

    (225 + 100 + 25 + 0 + 25 + 100 + 225) / 7

    = 100

    Remember, that's the *variance*. To get the standard deviation, take the square root.

    s.d. = √100

    s.d. = 10

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