Question

kiara went on 6 hikes. the hikes were: 3.8 miles 4.3 miles 2.2 miles 5.5 miles 2.4 miles 7.0 miles what was the mean absolute deviation of the lengths of kiaras hikes? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): miles

Explanation:

Step1: Calculate the mean of the data set.

The data set is \( 3.8, 4.3, 2.2, 5.5, 2.4, 7.0 \). The number of data points \( n = 6 \).
The mean \( \bar{x}=\frac{3.8 + 4.3+2.2 + 5.5+2.4 + 7.0}{6} \)
First, sum the values: \( 3.8+4.3 = 8.1 \), \( 8.1+2.2 = 10.3 \), \( 10.3+5.5 = 15.8 \), \( 15.8+2.4 = 18.2 \), \( 18.2+7.0 = 25.2 \)
Then, \( \bar{x}=\frac{25.2}{6}=4.2 \)

Step2: Find the absolute deviation of each data point from the mean.

For \( 3.8 \): \( |3.8 - 4.2|=0.4 \)
For \( 4.3 \): \( |4.3 - 4.2|=0.1 \)
For \( 2.2 \): \( |2.2 - 4.2|=2.0 \)
For \( 5.5 \): \( |5.5 - 4.2|=1.3 \)
For \( 2.4 \): \( |2.4 - 4.2|=1.8 \)
For \( 7.0 \): \( |7.0 - 4.2|=2.8 \)

Step3: Calculate the mean of these absolute deviations.

Sum of absolute deviations: \( 0.4+0.1 + 2.0+1.3+1.8+2.8 \)
\( 0.4 + 0.1=0.5 \), \( 0.5+2.0 = 2.5 \), \( 2.5+1.3 = 3.8 \), \( 3.8+1.8 = 5.6 \), \( 5.6+2.8 = 8.4 \)
Mean absolute deviation \( MAD=\frac{8.4}{6}=1.4 \)

Answer:

\( 1.4 \)