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in Mathematics by (64.9k points)

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :

Draw both ogives for the data above.

Hence obtain the median profit.

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We first draw the coordinate axes, with lower limits of the profit along the horizontal axis, and the cumulative frequency along the vertical axes. Then, we plot the points (5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7) and (35, 3). We join these points with a smooth curve to get the ‘more than’ ogive, as shown in Fig. 14.5. 

Now, let us obtain the classes, their frequencies and the cumulative frequency from the table above.

Using these values, we plot the points (10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27), (40, 30) on the same axes as in Fig. 14.5 to get the ‘less than’ ogive, as shown in Fig. 14.6.

The abcissa of their point of intersection is nearly 17.5, which is the median. This can also be verified by using the formula. Hence, the median profit (in lakhs) is Rs 17.5.

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