Question

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.

No. of bulbs produced (Thousands)	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
No. of factories	12	35	20	15	8	7	8

Answer 1

Class (Number of bulbs produced in thousands)	Frequency (Number of factories) fi	Cumulaive frequency less than the upper limit
30 - 40	12	12
40 - 50	35	47
50 - 60 (Median Class)	20	67
60 - 70	15	82
70 - 80	8	90
80 - 90	7	97
90 - 100	8	105
	N = 105

From the above table, we get

L (Lower class limit of the median class) = 50

N (Sum of frequencies) = 105

h (Class interval of the median class) = 10

f (Frequency of the median class) = 20

cf (Cumulative frequency of the class preceding the median class) = 47

Now, Median $=L+\frac{(\frac{N}{2}-Cf)}{f}\times h$

$=50+\frac{(\frac{105}{2}-47)}{20}\times 10$

= 50 + 2.75

= 52.75 thousand lamps

= 52750 lamps

Hence, the median of the productions is 52750 lamps.