Question

polinas math scores are shown in the table. polinas math scores math scores 72 65 75 88 90 what is the mean absolute deviation of her math scores? 5.4 7.8 8.8 6.4

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of numbers $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 5$, $x_1=72$, $x_2 = 65$, $x_3=75$, $x_4=88$, $x_5=90$.
$\bar{x}=\frac{72 + 65+75+88+90}{5}=\frac{390}{5}=78$.

Step2: Calculate the absolute deviations

The absolute deviation of each data - point $x_i$ from the mean $\bar{x}$ is $|x_i-\bar{x}|$.
For $x_1 = 72$: $|72 - 78|=6$.
For $x_2=65$: $|65 - 78| = 13$.
For $x_3=75$: $|75 - 78|=3$.
For $x_4=88$: $|88 - 78| = 10$.
For $x_5=90$: $|90 - 78|=12$.

Step3: Calculate the mean absolute deviation (MAD)

The mean absolute deviation $MAD=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$.
$\sum_{i = 1}^{5}|x_i-\bar{x}|=6 + 13+3+10+12=44$.
$MAD=\frac{44}{5}=8.8$.

Answer:

$8.8$