grace is looking at a report of her monthly cell - phone usage for the last year to determine if she needs…

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

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

Answer

Explanation:

Step1: Calculate the mean

First, sum all the data values: $700 + 735+680 + 890+755+740+670+785+805+1050+820+750=9280$. There are $n = 12$ data - points. The mean $\bar{x}=\frac{9280}{12}\approx773.33$.

Step2: Calculate the squared - differences

For each data value $x_i$, calculate $(x_i-\bar{x})^2$. For example, for $x_1 = 700$, $(700 - 773.33)^2=(-73.33)^2 = 5377.29$. Do this for all 12 data values and sum them up. $(700 - 773.33)^2+(735 - 773.33)^2+(680 - 773.33)^2+(890 - 773.33)^2+(755 - 773.33)^2+(740 - 773.33)^2+(670 - 773.33)^2+(785 - 773.33)^2+(805 - 773.33)^2+(1050 - 773.33)^2+(820 - 773.33)^2+(750 - 773.33)^2$ $=5377.29+1469.49+8710.89+13627.77+336.11+1110.89+10677.77+136.11+999.49+76544.89+2177.77+544.89 = 120015.88$.

Step3: Calculate the variance

The variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{120015.88}{11}\approx10910.54$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}=\sqrt{10910.54}\approx104.45\approx100$.

Answer:

100