Question

The upper quartile for the following distribution

Size of items	1	2	3	4	5	6	7
Frequency	2	4	5	8	7	3	2

is given by the size of

• A. $\left( \frac{31 + 1}{4} \right)$th item
• B. $\left\lbrack 2\left( \frac{31 + 1}{4} \right) \right\rbrack$th item
• C. $\left\lbrack 3\left( \frac{31 + 1}{4} \right) \right\rbrack$th item
• D. $\left\lbrack 4\left( \frac{31 + 1}{4} \right) \right\rbrack$th item

Answer 1

Answer: (C)

$\left\lbrack 3\left( \frac{31 + 1}{4} \right) \right\rbrack$th item

Answer 2

Upper Quartile = Size of $\left\lbrack 3\frac{(n + 1)}{4} \right\rbrack^{th}$item

= Size of $\left\lbrack 3\left( \frac{31 + 1}{4} \right) \right\rbrack^{th}$item, $\lbrack\because\Sigma f = 31\rbrack$.