Question

calculate the median for each data set.
set a 6 9 10 13 15 16 18 21
set b 9 11 14 15 16 19 24 29
set a: median = 15.5
set b: median = 14
set a: median = 14
set b: median = 15.5
set a: median = 13
set b: median = 15
set a: median = 15
set b: median = 16

Explanation:

Step1: Determine number of data points

Both Set A and Set B have $n = 8$ data - points. Since $n$ is even, the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th ordered data values.

Step2: Find median for Set A

For Set A, $\frac{n}{2}=\frac{8}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 13 and the 5th value is 15. Median of Set A=$\frac{13 + 15}{2}=\frac{28}{2}=14$.

Step3: Find median for Set B

For Set B, $\frac{n}{2}=\frac{8}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 15 and the 5th value is 16. Median of Set B=$\frac{15+16}{2}=15.5$.

Answer:

Set A: median = 14
Set B: median = 15.5