Questions: 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 3 years are listed below. 53, 65, 78, 127, 36, 19, 21, 78, 127, 58

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 3 years are listed below. 53, 65, 78, 127, 36, 19, 21, 78, 127, 58
Transcript text: 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 3 years are listed below. \[ \begin{array}{llllllllll} 53 & 65 & 78 & 127 & 36 & 19 & 21 & 78 & 127 & 58 \end{array} \]
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Solution

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Solution Steps

Step 1: Calculate the Mean
  • Add all the durations together: \( 53 + 65 + 78 + 127 + 36 + 19 + 21 + 78 + 127 + 58 \).
  • Count the number of data points: 10.
  • Divide the sum by the number of data points to find the mean.
Step 2: Determine the Median
  • Arrange the data in ascending order: \( 19, 21, 36, 53, 58, 65, 78, 78, 127, 127 \).
  • Since there are 10 data points (an even number), find the average of the 5th and 6th values in the ordered list.
Step 3: Identify the Mode
  • Look for the value(s) that appear most frequently in the data set.
  • Check if there is one or more values that occur with the highest frequency.

Final Answer

Mean: \( \boxed{65.5} \)
Median: \( \boxed{66.5} \)
Mode: \( \boxed{78 \text{ and } 127} \)

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