Question

grace is looking at a report of her monthly cell - phone usage for the last year to determine if she needs to upgrade her plan. the list represents the approximate number of megabytes of data grace used each month. 700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750. what is the standard deviation of the data? round to the nearest whole number. 65 75 100 130

Explanation:

Step1: Calculate the mean

The data set is \(700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750\).
The mean \(\bar{x}=\frac{700 + 735+680 + 890+755+740+670+785+805+1050+820+750}{12}=\frac{9280}{12}\approx773.33\)

Step2: Calculate the squared - differences

\((700 - 773.33)^2\approx5377.78\), \((735 - 773.33)^2\approx1469.44\), \((680 - 773.33)^2\approx8711.11\), \((890 - 773.33)^2\approx13627.78\), \((755 - 773.33)^2\approx336.11\), \((740 - 773.33)^2\approx1110.89\), \((670 - 773.33)^2\approx10677.78\), \((785 - 773.33)^2\approx136.11\), \((805 - 773.33)^2\approx992.78\), \((1050 - 773.33)^2\approx76544.44\), \((820 - 773.33)^2\approx2188.89\), \((750 - 773.33)^2\approx544.44\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{5377.78+1469.44 + 8711.11+13627.78+336.11+1110.89+10677.78+136.11+992.78+76544.44+2188.89+544.44}{12 - 1}=\frac{131719.86}{11}\approx11974.53\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{11974.53}\approx109.43\approx109\approx100\) (rounded to the nearest whole number)

Answer:

100