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  • The following table gives the distribution of the life time of 400 neon lamps :

5. The following table gives the distribution of the life time of 400 neon lamps :
3.5
Find the median life time of a lamp.

Answers (1)

best_answer

Class

Frequency

 f_i

Cumulative

Frequency
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

\dpi{100} N= 400 \implies \frac{N}{2} = 200
Therefore, Median class = 3000-3500

Lower limit, l = 3000; Class height, h = 500
Frequency corresponding to median class, f = 86
Cumulative frequency of the class preceding the median class, c.f. = 130

Median = l + \left (\frac{\frac{n}{2}-c.f}{f} \right ).W
\\ = 3000 + \left (\frac{200-130}{86} \right ).500 \\ \\ = 3000+406.97

= 3406.97

Thus, the median lifetime of a lamp is 3406.97 hours

Posted by

HARSH KANKARIA

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