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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 - Mathematics and Statistics

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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.

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Solution

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 P70.
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

Concept: Graphical Location of Partition Values
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