Question

Find the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.−10, −16, −21, −24, −4, −30, −32

Answer 1

The range is the largest number minus the smallest number

-4 - ( -32)

-4+32

28

First we need to find the mean

mean = sum / number of terms = -137/7 = -19.57142857

Then we find the variance

1/number of terms( sum ( term - mean) ^2) for each term

(1/7 [ (-10 - -19.57142857)^2 + (-16 - -19.57142857)^2+(-21 - -19.57142857)^2+(-24 - -19.57142857)^2+

(-4 - -19.57142857)^2 + (-30 - -19.57142857)^2 + (-32 - -19.57142857)^2]

1/7( 631.71428571429)

90.244897959184

To the nearest tenth

90.2

The standard deviation is the square root

sqrt( 90.244897959184)

9.4997314699407

To the nearest tenth

9.5