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The following table gives the distribution of the life time of 400 neon lamps :
Lifetime(in hours) Number of lamps
1500-2000 14
2000-2500 56
2500-3000 60
3000-3500 86
3500-4000 74
4000-4500 62
4500-5000 48
Find the median lifetime of a lamp.


Answer :

Class Interval Frequency Cumulative
1500-2000 14 14
2000-2500 56 70
2500-3000 60 130
3000-3500 86 216
3500-4000 74 290
4000-4500 62 352
4500-5000 48 400

n = 400
\(\Rightarrow \frac{n}{2} \ = \ 200 \)

Median class = 3000 - 3500

\(\therefore \) \( l = 3000, cf = 130, f = 86, h = 500 \)

Median \( = \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h \)

Median \(= \ 3000 \ + \ ( \frac{200 \ - \ 130}{86}) \ × \ 500 \)

\(= \ 3000 \ + \ \frac{70}{86} \ × \ 500 \)

\(= \ 3000 \ + \ 406.98 \)

\(= \ 3406.98 \)

\(\therefore \) median lifetime of lamps = 3406.98 hours

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