Find the first and third quartiles for the following data.

12, 5, 7, 3, 1, 13, 17, 5, 19, 13, 1

Q_{1} = 3, Q_{3} = 13

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Q_{1} = 13, Q_{3} = 3

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Q_{1} = 3, Q_{3} = 9

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Q_{1} = 9, Q_{3} = 3

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Solution

The correct option is A $Q_{1} = 3, Q_{3} = 13$
Arrange the data in ascending order.

1, 1, 3, 5, 5, 7, 12, 13, 13, 17, 19

Here, N = 11
$Q_{1} = S i z e o f (\frac{N + 1}{4}) t h o b s e r v a t i o n = s i z e o f 3 r d o b s e r v a t i o n = 3$

$Q_{3} = S i z e o f 3 (\frac{N + 1}{4}) t h o b s e r v a t i o n = s i z e o f 9 t h o b s e r v a t i o n = 13$

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