Question

1.5 cool down
data: 5, 18, 6, 18, 13
mean: 12

1. find the mean absolute deviation for the data.
2. find the interquartile range for the data.

Explanation:

Step1: Calculate absolute deviations

Find the absolute difference between each data - point and the mean.
$|5 - 12|=7$, $|18 - 12| = 6$, $|6 - 12|=6$, $|18 - 12| = 6$, $|13 - 12|=1$

Step2: Calculate the mean absolute deviation (MAD)

Sum the absolute deviations and divide by the number of data - points.
$MAD=\frac{7 + 6+6 + 6+1}{5}=\frac{26}{5}=5.2$

Step3: Arrange data in ascending order

$5,6,13,18,18$

Step4: Find the median (Q2)

Since there are 5 data - points, the median is the 3rd value. So, $Q2 = 13$.

Step5: Find Q1 and Q3

The lower half of the data is $5,6$. The median of the lower half ($Q1$) is $\frac{5 + 6}{2}=5.5$.
The upper half of the data is $18,18$. The median of the upper half ($Q3$) is $\frac{18+18}{2}=18$.

Step6: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=18 - 5.5 = 12.5$

Answer:

1. $5.2$
2. $12.5$