Find the median lifetime of a lamp.

NCERT Class 10 Math’s Chapter 14

Page No. 289

Exercise 14.3

Question No. 5

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The cumulative frequencies with their respective class intervals are as follows.

It can be observed that the cumulative frequency just greater than n/2 (i.e.400/2 = 200) is 216, belonging to class interval 3000 – 3500.

Median class = 3000 – 3500

Lower limt (l) of median class = 3000

Frequency (f) of median class = 86

Cumulative frequency (cf) of class preceding median class = 130

Class size = 500

Median = l + ((n/2 – cf)/f) × h = 3000 + ((200 – 130)/86) × 500 = 3000 + 35000/86 = 3000 + 406.978 + 3406.978

Therefore, median lifetime of lamps is 3406.98 hours.