Question

students reported volunteering at the animal shelter during the last 6 months for 25, 36, 31, and 32 hours. what is the mean absolute deviation for the number of hours students volunteered? round to the nearest tenth.
0
3
4
6

Explanation:

Step1: Calculate the mean

First, find the mean (\(\bar{x}\)) of the data set. The data points are 25, 36, 31, and 32. The formula for the mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 4\) (the number of data points) and \(x_{i}\) are the individual data points.

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Step2: Find the absolute deviations

Next, find the absolute deviation of each data point from the mean. The absolute deviation of a data point \(x_{i}\) is \(|x_{i}-\bar{x}|\).

• For \(x_{1}=25\): \(|25 - 31|=|-6| = 6\)
• For \(x_{2}=36\): \(|36 - 31|=|5| = 5\)
• For \(x_{3}=31\): \(|31 - 31|=|0| = 0\)
• For \(x_{4}=32\): \(|32 - 31|=|1| = 1\)

Step3: Calculate the mean of the absolute deviations

Now, find the mean of these absolute deviations. The formula for the mean absolute deviation (MAD) is \(MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}\).

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Answer:

3 (corresponding to the option "3")