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

First, sum all the data points and divide by the number of data points ($n=12$):
Sum = $700 + 735 + 680 + 890 + 755 + 740 + 670 + 785 + 805 + 1050 + 820 + 750 = 9380$
Mean $\bar{x} = \frac{9380}{12} \approx 781.67$

Step2: Find squared differences

Calculate $(x_i - \bar{x})^2$ for each data point:
$(700-781.67)^2 \approx 6669.99$, $(735-781.67)^2 \approx 2178.09$, $(680-781.67)^2 \approx 10336.79$,
$(890-781.67)^2 \approx 11735.39$, $(755-781.67)^2 \approx 711.29$, $(740-781.67)^2 \approx 1736.39$,
$(670-781.67)^2 \approx 12470.19$, $(785-781.67)^2 \approx 11.09$, $(805-781.67)^2 \approx 544.29$,
$(1050-781.67)^2 \approx 71999.09$, $(820-781.67)^2 \approx 1469.19$, $(750-781.67)^2 \approx 1002.99$

Step3: Sum squared differences

Sum of squared differences $\approx 6669.99+2178.09+10336.79+11735.39+711.29+1736.39+12470.19+11.09+544.29+71999.09+1469.19+1002.99 = 120864.88$

Step4: Compute variance

Sample variance $s^2 = \frac{\text{Sum of squared differences}}{n-1} = \frac{120864.88}{11} \approx 10987.72$

Step5: Calculate standard deviation

Standard deviation $s = \sqrt{10987.72} \approx 104.82$, rounded to the nearest whole number is 100.

Answer:

○ 100