The annual profits earned by $30$ shops of a shopping complex in a locality give rise to the following distribution:
Profit (Rs in lakhs) Number of shops (frequency) More than or equal to $5$ $30$ More than or equal to $10$ $28$ More than or equal to $15$ $16$ More than or equal to $20$ $14$ More than or equal to $25$ $10$ More than or equal to $30$ $7$ More than or equal to $35$ $3$
Draw both ogives for the data above. Hence,obtain the median profit.
| Profit (Rs in lakhs) | Number of shops (frequency) |
| More than or equal to $5$ | $30$ |
| More than or equal to $10$ | $28$ |
| More than or equal to $15$ | $16$ |
| More than or equal to $20$ | $14$ |
| More than or equal to $25$ | $10$ |
| More than or equal to $30$ | $7$ |
| More than or equal to $35$ | $3$ |
Draw both ogives for the data above. Hence,obtain the median profit.
(17.5) To draw the 'more than' ogive,we plot the points $(5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7),$ and $(35, 3)$ on a graph where the horizontal axis represents the lower limits of profit and the vertical axis represents the cumulative frequency. We join these points with a smooth curve.
Next,we convert the given data into a frequency distribution table:
To draw the 'less than' ogive,we plot the points $(10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27),$ and $(40, 30)$ on the same axes.
The abscissa of the point of intersection of the two ogives gives the median. From the graph,the point of intersection is at $x = 17.5$. Therefore,the median profit is $Rs. 17.5$ lakhs.
Next,we convert the given data into a frequency distribution table:
| Classes | $5-10$ | $10-15$ | $15-20$ | $20-25$ | $25-30$ | $30-35$ | $35-40$ |
| No. of shops | $2$ | $12$ | $2$ | $4$ | $3$ | $4$ | $3$ |
| Cumulative frequency | $2$ | $14$ | $16$ | $20$ | $23$ | $27$ | $30$ |
To draw the 'less than' ogive,we plot the points $(10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27),$ and $(40, 30)$ on the same axes.
The abscissa of the point of intersection of the two ogives gives the median. From the graph,the point of intersection is at $x = 17.5$. Therefore,the median profit is $Rs. 17.5$ lakhs.
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In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times h$ for the median,$l = \ldots \ldots \ldots$
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