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Q16. The following distribution gives the annual profit camned by 30 shops of a shopping complex
Profit (Rs in lakhs)
5 - 10
10 - 15
15 -20
20-25
25-30
30 - 35
35 - 10
Total
No. of shops
2
12
2
4
3
3
30
Convert the distribution above to a less than type cumulative frequency distribution.
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Less Than Cumulative Frequency distribution table & Graph Of Less Than Ogive Is In The Attachment.
From the table : Plot these points (10,2)(15,14)(20,16)(25,20)(30,23)(35,27)(40,30) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.
More Than Cumulative Frequency distribution table & Graph Of more Than Ogive Is In The Attachment.
From the table : Plot these points (5,30)(10,28)(15,16)(20,14)(25,10)(30,7) and (35,3) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.
The two ogives intersect at a point. We draw a perpendicular line from this point to x-axis , the intersection point on x-axis is 17.5 .
Hence, the required median is ₹ 17.5 lakh.
★★ LESS THAN TYPE OGIVE:
It is the graph drawn between upper limits and cumulative frequencies of a distribution. Here, we mark the points with upper limit and x- coordinate and corresponding cumulative frequency as y- coordinate and join them by freehand smooth curve. This type of graph is cumulated upward.
★★ MORE THAN TYPE OGIVE:
It is the graph drawn between lower limits and cumulative frequencies of a distribution. Here we mark the points with lower limit and x- coordinate and corresponding cumulative frequency and y- coordinate and join them by freehand smooth curve. This type of graph is cumulated downward.
★★ If we have both ogives (less than type and more than type) then these two ogives intersect each other at a point . From this point , draw a perpendicular on x-axis the point at which it cuts x-axis gives the median i.e the x-coordinate of intersection point gives the median.
Step-by-step explanation:
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