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
Answer
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
For each data point (x_i), calculate ((x_i-\bar{x})^2). For example, for (x_1 = 700), ((700 - 773.33)^2=(- 73.33)^2 = 5377.7889). Do this for all 12 data points.
Step3: Calculate the variance
The variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n}), where (n = 12). After calculating the sum of the squared - differences and dividing by 12, we get (s^2\approx10739.81).
Step4: Calculate the standard deviation
The standard deviation (s=\sqrt{s^2}). So (s=\sqrt{10739.81}\approx103.63\approx100) (rounded to the nearest whole number).
Answer:
100