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 No. of bulbs produced (in thousands)	Frequency (Number of factories) fi	Cumulaive frequency (less than)
30 - 40	12	12
40 - 50	35	47→cf
50 - 60 (Median Class)	20→f	67
60 - 70	15	82
70 - 80	8	90
80 - 90	7	97
90 - 100	8	105
Total	N = 105

Here, total frequency = Σf_i = N = 105

∴ `"N"/2 = 105/2 = 52.5`

Cumulative frequency which is just greater than (or equal) to 52.5 is 67.

∴ The median class is 50 – 60.

Now, L = 50, f = 20, cf = 47, h = 10.

∴ Media = `"L" + (("N"/2 - "cf")/"f") × h`

`= 50 + ((52.5 - 47)/20) × 10`

`= 50 + ((5.5)/20) × 10`

= 50 + 2.75

= 52.75 thousand lamps

= 52.75 × 1000

= 52750 lamps

Hence, the median of the productions is 52750 lamps.