Question

1. the data below represents the number of canoes rented each month from may through october. find the mean absolute deviation. round to the nearest hundredth. {15, 29, 36, 45, 31, 12}

Explanation:

Step1: Calculate the mean

First, find the sum of the data set: \(15 + 29 + 36 + 45 + 31 + 12 = 168\)
There are 6 data points, so the mean \(\bar{x}=\frac{168}{6}=28\)

Step2: Find the absolute deviations

Calculate the absolute difference between each data point and the mean:

• \(|15 - 28| = 13\)
• \(|29 - 28| = 1\)
• \(|36 - 28| = 8\)
• \(|45 - 28| = 17\)
• \(|31 - 28| = 3\)
• \(|12 - 28| = 16\)

Step3: Calculate the mean of these absolute deviations

Sum the absolute deviations: \(13 + 1 + 8 + 17 + 3 + 16 = 58\)
Then divide by the number of data points: \(\text{Mean Absolute Deviation}=\frac{58}{6}\approx9.67\)

Answer:

\(9.67\)