Question
Measures of Question 11, 2.3.24 HW Score: \( 39.81 \%, 7.17 \) of 18 points Part 1 of 6 Points: 0 of 1 Save Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. The durations (in minutes) of power failures at a residence in the last 5 years are listed below. \[ \begin{array}{llllllllll} 87 & 42 & 122 & 14 & 122 & 22 & 35 & 46 & 63 & 63 \end{array} \] What is the mean duration? Select the correct choice below and fill in any answer box to complete your choice. A. The mean duration is \( \square \) minutes. (Round to one decimal place as needed.) B. There is no mean score.
Ask by Edwards Malone. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The mean duration is 61.6 minutes.
Solution
To find the **mean** duration of the power failures, follow these steps:
1. **List of Durations (in minutes):**
\[
87, \ 42, \ 122, \ 14, \ 122, \ 22, \ 35, \ 46, \ 63, \ 63
\]
2. **Calculate the Sum of All Durations:**
\[
87 + 42 + 122 + 14 + 122 + 22 + 35 + 46 + 63 + 63 = 616 \ \text{minutes}
\]
3. **Count the Number of Data Points:**
\[
10 \ \text{durations}
\]
4. **Compute the Mean:**
\[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Data Points}} = \frac{616}{10} = 61.6 \ \text{minutes}
\]
**Answer Choice:**
**A. The mean duration is \( 61.6 \) minutes.**
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Simplify this solution Beyond the Answer
To find the mean, you sum up all the durations and then divide by the number of entries. Adding them together gives you 522 minutes. Since there are 10 durations, you divide 522 by 10, which gives you a mean of 52.2 minutes. So, the answer is A, with the mean duration being approximately \( 52.2 \) minutes. As for the median, you first need to arrange the data in ascending order: 14, 22, 35, 42, 46, 52, 63, 63, 87, 122, 122. The median is the middle value, which, in this case, falls between the 5th and 6th values, giving a median of \( 52.0 \) minutes. The mode is \( 63 \) and \( 122 \), since they appear more frequently than the others.
