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.
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○ 3
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○ 6

Explanation:

Step1: Find the mean

First, we calculate the mean (\(\bar{x}\)) of the data set \(25, 36, 31, 32\). The formula for the mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n\) is the number of data points and \(x_{i}\) are the data values.
\(n = 4\), \(\sum_{i=1}^{4}x_{i}=25 + 36+31 + 32=124\)
\(\bar{x}=\frac{124}{4}=31\)

Step2: Calculate the absolute deviations

For each data point \(x_{i}\), we find the absolute deviation \(|x_{i}-\bar{x}|\):

• 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: Find the mean of the absolute deviations

The formula for the mean absolute deviation (MAD) is \(MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}\)
\(\sum_{i = 1}^{4}|x_{i}-\bar{x}|=6 + 5+0 + 1=12\)
\(MAD=\frac{12}{4}=3\)

Answer:

3