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Find the Lower Quartile, the Upper Quartile, the Interquartile Range and the Semi-interquartile Range for the Following Frequency Distributions: Shoe Size 5 6 7 8 9 10 11 Frequency 8 1 7 14 11 5 4 - Mathematics

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प्रश्न

Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions: 

Shoe size  5 6 7 8 9 10 11
Frequency 8 1 7 14 11 5 4
योग
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उत्तर

Shoe size  Frequency (f) Cumulative frequency
5 8 8
6 1 9
7 7 16
8 14 30
9 11 41
10 5 46
11 4 50

No. of terms = 50 

Lower Quartile (Q1) = `n/4 = 50/4` = 12.5th term = 7

Upper Quartile (Q3) = `(n xx 3)/4 = (50 xx 3)/4` = 37.5th term = 9

Interquartile range = Q3 - Q1 = 9-7 = 2 

Semi-interquartile range = `(Q_3 - Q_1)/2 = (9-7)/2 = 1`

Hence, Lower quartile = 7, upper quartile = 9, interquartile range = 2, semi-interquartile range = 1 

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अध्याय 24: Measures Of Central Tendency - Exercise

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फ्रैंक Mathematics - Part 2 [English] Class 10 ICSE
अध्याय 24 Measures Of Central Tendency
Exercise | Q 8.01

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