Question

stacy went on 7 hikes. the hikes were:
4.7 miles 2.7 miles 4.8 miles 9.3 miles 5.1 miles 6.1 miles 6.5 miles
what was the mean absolute deviation of the lengths of stacys hikes?
if the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (mad): miles

Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Here, $n = 7$, and $x_{1}=4.7,x_{2}=2.7,x_{3}=4.8,x_{4}=9.3,x_{5}=5.1,x_{6}=6.1,x_{7}=6.5$.
$\bar{x}=\frac{4.7 + 2.7+4.8 + 9.3+5.1+6.1+6.5}{7}=\frac{39.2}{7}=5.6$

Step2: Calculate the absolute deviations

$|4.7 - 5.6|=0.9$, $|2.7 - 5.6| = 2.9$, $|4.8 - 5.6|=0.8$, $|9.3 - 5.6|=3.7$, $|5.1 - 5.6|=0.5$, $|6.1 - 5.6|=0.5$, $|6.5 - 5.6|=0.9$

Step3: Calculate the mean of absolute deviations

$MAD=\frac{0.9+2.9 + 0.8+3.7+0.5+0.5+0.9}{7}=\frac{10.2}{7}\approx1.5$

Answer:

$1.5$