QuIz
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TIME REMAININC
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57:04

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.

What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130

Ask by Gibbs Ray. in the United States

Jan 22,2025

Question

QuIz
Active
TIME REMAININC
1
2
3
4
5
57:04

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.

What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130

Ask by Gibbs Ray. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To determine the standard deviation of Grace's monthly cell-phone usage, follow these steps:

1. **List the Data:**
   $$
   700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
   $$
   
2. **Calculate the Mean:**
   $$
   \text{Mean} = \frac{700 + 735 + 680 + 890 + 755 + 740 + 670 + 785 + 805 + 1050 + 820 + 750}{12} = \frac{9380}{12} \approx 781.67 \text{ MB}
   $$

3. **Compute Each Squared Deviation from the Mean:**
   $$
   \begin{align*}
   (700 - 781.67)^2 &\approx 6669.44 \
   (735 - 781.67)^2 &\approx 2177.78 \
   (680 - 781.67)^2 &\approx 10336.11 \
   (890 - 781.67)^2 &\approx 11736.11 \
   (755 - 781.67)^2 &\approx 711.11 \
   (740 - 781.67)^2 &\approx 1736.11 \
   (670 - 781.67)^2 &\approx 12369.44 \
   (785 - 781.67)^2 &\approx 11.11 \
   (805 - 781.67)^2 &\approx 544.44 \
   (1050 - 781.67)^2 &\approx 71957.44 \
   (820 - 781.67)^2 &\approx 1469.44 \
   (750 - 781.67)^2 &\approx 1002.78 \
   \end{align*}
   $$

4. **Sum of Squared Deviations:**
   $$
   \text{Total} \approx 120,721.32
   $$

5. **Calculate the Variance:**
   $$
   \text{Variance} = \frac{120,721.32}{12} \approx 10,060.11
   $$

6. **Determine the Standard Deviation:**
   $$
   \text{Standard Deviation} = \sqrt{10,060.11} \approx 100.3 \text{ MB}
   $$
   
   Rounding to the nearest whole number gives **100 MB**.

**Answer:** 100
The standard deviation of Grace's monthly cell-phone usage is **100 MB**.

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