Question

The following frequency distribution shows the profit (in ₹) of shops in a particular area of city:

Profit per shop (in ‘000)	No. of shops
0 – 10	12
10 – 20	18
20 – 30	27
30 – 40	20
40 – 50	17
50 – 60	6

Find graphically The limits of middle 40% shops.

Answer 1

The less than cumulative frequency table is

Profit per shop (in ‘000)	No. of shops (f)	Cumulative Frequency (less than type)
0 – 10	12	12
10 – 20	18	30
20 – 30	27	57
30 – 40	20	77
40 – 50	17	94
50 – 60	6	100
Total	100

Points to be plotted are (10, 12), (20, 30), (30, 57), (40, 77), (50, 94), (60, 100).

The middle 40% shops will lie between the limits given by P₃₀ and P_70.
N = 100
For P₃₀ `(30"N")/(100)=(30(100))/(100)` = 30

For P₇₀ `(70"N")/(100)=(70(100))/(100)` = 70
∴ We take the points having Y co-ordinates 30 and 70 on Y-axis. From these points, we draw lines parallel to X-axis. From the points where these lines intersect the curve, we draw perpendiculars on X-axis.
X-Co-ordinates of these points gives the values of P₃₀ and P₇₀.
∴ P₃₀ ≈ 20, P₇₀ ≈ 36