Question

a teacher used a word count tool to note the number of words in the papers submitted by 5 students: 997 words, 132 words, 279 words, 174 words, 374 words. what was the mean absolute deviation of the numbers of words written? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): words

Explanation:

Step1: Calculate the mean

First, find the sum of the word - counts: $997 + 132+279 + 174+374=1956$. Then, divide by the number of data points ($n = 5$). The mean $\bar{x}=\frac{1956}{5}=391.2$.

Step2: Calculate the absolute deviations

For $997$: $|997 - 391.2|=605.8$.
For $132$: $|132 - 391.2|=259.2$.
For $279$: $|279 - 391.2|=112.2$.
For $174$: $|174 - 391.2|=217.2$.
For $374$: $|374 - 391.2|=17.2$.

Step3: Calculate the mean of the absolute deviations

Find the sum of the absolute deviations: $605.8+259.2 + 112.2+217.2+17.2 = 1211.6$. Then, divide by the number of data points ($n = 5$). The mean absolute deviation $MAD=\frac{1211.6}{5}=242.32\approx242.3$.

Answer:

$242.3$