Find the median life time of a bulb from the following data:

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Solution

Life time(in hours)

Number of bulbs

C.f(position)

0-250

6

6

250-500

10

16

500-750

11

27

750-1000

15

42

1000-1250

10

52

1250-1500

5

57

Sum of number of bulbs $57 (o d d) - \frac{57}{2} = 28.5 M e d i a n = l + ⎛ ⎜ ⎜ ⎝ \frac{\frac{n}{2} - c . f}{f} ⎞ ⎟ ⎟ ⎠ \times h L = l o w e r b o u n d a r y o f m e d i a n c l a s s f = f r e q u e n c y o f t h e m e d i a n c l a s s h = w i d t h o f t h e m e d i a n c l a s s c . f = c u m u l a t i v e f r e q u e n c y o f t h e c l a s s o f m e d i a n c l a s s n = t o t a l f r e q u e n c y M e d i a n = 750 + (\frac{28.5 - 27}{15}) \times 250 = 750 + (\frac{3 \times 250}{2 \times 15}) = 750 + 25 = 775 A n s$

Suggest Corrections

Life (in Hrs.)	0-20	20-40	40-60	60-80	80-100	100-120
No. of electric bulbs	31	36	38	42	82	71