Question

semi interquartile range of the data 3,4,6,9,11,12,14,15.

Answer 1

Answer:

Semi Interquartile range = 4

Explanation:

To find Interquartile range of 3,4,6,9,11,12,14,15

1) Arrange the data in ascending order

3,4,6,9,11,12,14,15

2) Find median of the data,for that count number of data points

n = 8

Median of even number:

Average of $\frac{n}{2}$ th and $(\frac{n}{2} +1)th$ term

$\frac{8}{2}th$ = 4 th term = 9

4th +1 = 5th term = 11

Median = $\frac{9+11}{2}$

Median = 10

Now Quartile 1 (Q₁), left part of median = $\frac{4+6}{2} = \frac{10}{2}$ = 5

Quartile 3 (Q₃), right part of median = $\frac{12+14}{2} = \frac{26}{2}$ = 13

Interquartile Range  = IQR = (Q₃- Q₁) = 13-5= 8

Now find

semi interquartile range = $\frac{8}{2}  = 4$