Question

emmetts class helped clean up a local beach. the 6 students in the class each filled their trash bags with varying amounts of litter: 52 pieces 70 pieces 52 pieces 99 pieces 47 pieces 70 pieces. what was the mean absolute deviation of the amounts of litter collected? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): pieces

Explanation:

Step1: Calculate the mean

The data set is \(52,70,52,99,47,70\). The mean \(\bar{x}=\frac{52 + 70+52+99+47+70}{6}=\frac{390}{6}=65\).

Step2: Calculate the absolute - deviations

For \(52\): \(|52 - 65|=13\); for the first \(70\): \(|70 - 65| = 5\); for the second \(52\): \(|52 - 65|=13\); for \(99\): \(|99 - 65| = 34\); for \(47\): \(|47 - 65|=18\); for the second \(70\): \(|70 - 65| = 5\).

Step3: Calculate the mean of the absolute - deviations

The sum of the absolute - deviations is \(13+5+13+34+18+5 = 88\). The mean absolute deviation \(MAD=\frac{88}{6}\approx14.7\).

Answer:

\(14.7\)