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Lorenz Curve

In the follow...

Question

In the following table is given, the number of companies belonging to two areas A and B according to the amounts of profits earned by them. Draw their Lorenz curve.

$\begin{matrix} Profits Earned (Rs in 000) & Area A & Area B 6 & 6 & 2 25 & 11 & 38 60 & 13 & 52 84 & 14 & 28 105 & 15 & 38 150 & 17 & 26 170 & 10 & 12 400 & 14 & 4 \end{matrix}$

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Solution

Number of Companies

$\begin{matrix} Profit & Cumulative & Percentage & Area A & Cumulative & Precentage & Area B & Cumulative & Percentage (thousand) & frequency & frequency & frequency 6 & 6 & 6 & 6 & 6 & 6 & 2 & 2 & 1 25 & 31 & 3.1 & 11 & 17 & 17 & 38 & 40 & 20 60 & 91 & 9.1 & 13 & 30 & 30 & 52 & 92 & 46 84 & 175 & 17.5 & 14 & 14 & 44 & 28 & 120 & 60 105 & 430 & 43 & 17 & 76 & 76 & 26 & 184 & 92 170 & 600 & 60 & 10 & 86 & 86 & 12 & 196 & 98 400 & 1000 & 100 & 14 & 100 & 100 & 4 & 200 & 100 \end{matrix}$

A lorenz curve is shown below

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Q. The following table shows number of firms in two different areas 'A' and 'B' according to their annual profits. Present the data by way of Lorenz curve.

Profit ('000' ₹)	6	25	60	84	105	150	170	400
Firms in Area A	6	11	13	14	15	17	10	14
Firms in Area B	2	38	52	28	38	26	12	4

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\begin{matrix} ↓ Y e a r / \to R e v e n u e (i n l a k h s) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 1971 & 3 & 4 & 2 & 1 1981 & 5 & 7 & 4 & 3 1991 & 10 & 8 & 7 & 4 2001 & 12 & 10 & 10 & 6 2011 & 14 & 12 & 18 & 11 \end{matrix}

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No. of companies	$4$	$28$	$49$	$17$	$2$

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