Question

find the mean absolute deviation
15, 17, 15, 17, 21, 17, 15, 23, 20, 18
(data | mean | difference | positive value)

Explanation:

Step1: Calculate the mean

Sum of data: $15+17+15+17+21+17+15+23+20+18=180$
Mean $\mu=\frac{180}{10}=18$

Step2: Find absolute differences

Compute $|x-\mu|$ for each data point:
$|15-18|=3$, $|17-18|=1$, $|15-18|=3$, $|17-18|=1$, $|21-18|=3$, $|17-18|=1$, $|15-18|=3$, $|23-18|=5$, $|20-18|=2$, $|18-18|=0$

Step3: Calculate MAD

Sum of absolute differences: $3+1+3+1+3+1+3+5+2+0=22$
MAD $=\frac{22}{10}=2.2$

Answer:

2.2