Question

the following table shows the number of raisins in a scoop of a variety of brands of raisin bran cereal.
brand number of raisins
generic 5
claytons 9
good2go 5
right from nature 5
morning meal 7
mmmm 11
find the mean absolute deviation (mad) of the data set.
raisins

Explanation:

Step1: Calculate the mean

First, we find the sum of the number of raisins: \(5 + 9 + 5 + 5 + 7 + 11 = 42\). There are 6 data points, so the mean \(\bar{x}=\frac{42}{6}=7\).

Step2: Find absolute deviations

For each data point, calculate the absolute deviation from the mean:

• \(|5 - 7| = 2\)
• \(|9 - 7| = 2\)
• \(|5 - 7| = 2\)
• \(|5 - 7| = 2\)
• \(|7 - 7| = 0\)
• \(|11 - 7| = 4\)

Step3: Calculate the mean of absolute deviations

Sum these absolute deviations: \(2 + 2 + 2 + 2 + 0 + 4 = 12\). Then divide by the number of data points (6): \(\text{MAD}=\frac{12}{6}=2\).

Answer:

2