Question

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

Answer 1

Consider the data 3,4,6,9,11,12,14,15.

Let us arrange the data in ascending order, we get

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

Let us find the median of the given data.

Since, there are 8 terms in the given data.

Let us find  $\frac{n}{2} term = \frac{8}{2} = 4$ th term = 9

Now, we will find $\frac{n}{2} + 1 = 4+1 =5$th term = 11

So, Median = Mean of 4th and 5th term  

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

= 10

Now, Semi interquartile range = $\frac{Q_3 -Q_1}{2}$

$Q_3$ is calculated by finding median of first half of the data that is mean of 3,4,6,9

$Q_3 = \frac{4+6}{2}$ = 5

$Q_1$ is calculated by finding median of second half of the data that is mean of 11,12,14,15

$Q_1 = \frac{12+14}{2}$ = 13

So, semi interquartile range = $\frac{13-5}{2}$

= 4.

Therefore, the semi interquartile range of the data is 4.