Question

The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices.

Price (Rupees)	20 less than	20 - 40	40 - 60	60 - 80	80 - 100
No. of articles	140	100	80	60	20

In a general store, the prices of different articles and their demand are shown in the following frequency distribution table. Find the median of the prices.

Prices in rupees	No. of articles
Less than 20	140
20-40	100
40-60	80
60-80	60
80-100	20

Answer 1

Class (Prices in rupees)	Frequency (Number of articles) (fi)	Cumulative frequency less than the upper limit
20 less than	140	140 → cf
20 - 40	100 → f	240
40 - 60	80	320
60 - 80	60	380
80 - 100	20	400
Total	N = 400

From the above table, we get

∑f_i = N = 400

∴ `N/2 = 400/2 = 200`

∴ The cumulative frequency greater than (or equal to) 200 is 240.

∴ 20 – 40 is the median class.

Now, L = 20, f = 100, c.f. = 140, h = 20

Now, Median = `L + [(N/2 - c.f.)/f] xx h`

= `20+ ((200-140)/100) xx20`

= `20 + (60/100) xx 20`

= 20 + 12

= ₹ 32

Hence, the median of the prices of an article is ₹ 32.