First slide

Introduction to statistics

Question

The semi-interquartile range of the data 3, 6, 5, 4, 2, 1, 7 is

Moderate

A

4
B

3
C

2
D

1

Solution

Arranging the data in ascending order, we obtain
1, 2, 3, 4, 5, 6, 7
$∴ Q_{1} =$ Value of ${(\frac{n + 1}{4})}^{t h}$ observation
$\Rightarrow Q_{1} =$ Value of 2nd observation = 2
$Q_{3} =$ Value of $3 {(\frac{n + 1}{4})}^{t h}$ observation
$\Rightarrow Q_{3} =$ Value of 6th observation= 6
$∴$ Semi-interquartile range $= \frac{Q_{3} - Q_{1}}{2} = 2$

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