Question

50.
Find Q1 for the following observations 14, 16, 13, 15, 20, 18, 19,22
(a) 14
(b) 14.25
(c) 15
(d) 15.25
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Answer 1

Step-by-step explanation:

q1 = n+1/4

q1 = 8+1/4 = 2.25

13,14,15,16,18,19,20,22

= 13+2.25 = 15.25

Answer d) 15.25

Answer 2

CORRECT QUESTION

Find Q1 for the following observations 14, 16, 13, 15, 20, 18, 19,22

(a) 14

(b) 14.5

(c) 15

(d) 15.25

ANSWER

The correct answer is option(b) 14.5

GIVEN

Set of observation - 14, 16, 13, 15, 20, 18, 19,22

TO FIND

Q1 (lower quartile) of the data.

SOLUTION

We can simply solve the above problem as follows -

the lower quartile is the value when 25% of the set of data is found when arranged in ascending order.

To find the Q1, we will do the following steps :

Arrange the data into ascending order -

13, 14, 15, 16, 18, 19, 20, 22

We will find the median of the following data -

so, if x1 = 13 and x2 = 14

so the median will be the mean of x4 and x5

median = 16+18/2 = 17

Now, the lower quartile will be the median of the upper half of the data

So,

$Q1 = \frac{x1 + x2}{2}$

$Q1 = \frac{14 + 15}{2} = 14.5$

Hence, the lower quartile (Q1) is 14.5

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