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Question
The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q1 and Q3 for above data.
Solution
The given data can be arranged in ascending order as follows:
145, 148, 151, 152, 154, 158, 159, 163, 171, 171.
Here, n = 10
Q1 = value of `(("n" + 1)/4)^"th"`observation
= value of `((10 + 1)/4)^"th"`observation
= value of (2.75)th observation
= value of 2nd observation + 0.75 (value of 3rd observation – value of 2nd observation)
= 148 + 0.75 (151 – 148)
= 148 + 0.75 (3)
= 148 + 2.25
∴ Q1 = 150.25
Q3 = value of `3("n+1"/4)^"th"`observation
= value of `3((10 + 1)/4)^"th"`observation
= value of (3 × 2.75)th observation
= value of (8.25)th observation
= value of 8th observation + 0.25 (value of 9th observation – value of 8th observation)
= 163 + 0.25 (171 – 163)
= 163 + 0.25 (8)
= 163 + 2
∴ Q3 = 165
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