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The ages of a group of lifeguards are listed. 17, 17, 18, 19, 22, 23, 25, 27, 32, 38 If another age of 24 is added to the data, how would the mean be impacted? The mean would stay the same value of about 22.5. The mean would stay the same value of about 23.8. The mean would increase in value to about 23.5. The mean would decrease in value to about 24.2.

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Answer:

The mean would stay the same value of about 23.8

Explanation:

Step 1: Determine the mean of the ages before 24 is added:

The mean is defined as the average of a set of data.

We calculate it by dividing the sum of the data by the total number of data points.

Since there are 10 data points before the 24 is added, we can find the mean by dividing the sum of these 10 data points by 10:

Mean (without 24) = (17 + 17 + 18 + 19 + 22 + 23 + 25 + 27 + 32 + 38) / 10

Mean (without 24) = (238) / 10

Mean (without 24) = 23.8

Thus, the mean without the 24 is 23.8.

Step 2: Determine the mean with the 24 added:

Since the sum before the 24 is added is 238 and adding the 24 means that there are now 11 data points, we can divided the sum of 238 and 24 by 11 to find the mean with the 24 added:

Mean (with 24) = (238 + 24) / (10 + 1)

Mean (with 24) = (262) / 11

Mean (with 24) = 23.81818182

Thus, the mean with the 24 is about 23.82.

Step 3: Determine how the mean changes:

Since the mean without the 24 is 23.8 and the mean with the 24 is 23.82, the mean would stay the same value of about 23.8.

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