Question

The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution:
Profit (In lakhs In Rs) 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 ogive for the above data and hence obtain the median.

Answer 1

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.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

For more than method:

Now, we mark on x-axis lower class limits, y-axis cumulative frequency

Thus, we plot the points (5,30),(10,28),(15,16),(20,14),(25,10),(30,7)and(35,3)

Less than method:

Profit in lakhs No. of shops Profit less than C.F

0−10 2 10 2

10−15 12 15 14

15−20 2 20 16

20−25 4 25 20

25−30 3 30 23

30−35 4 35 27

35−40 3 40 30

Now we mark the upper class limits along x-axis and cumulative frequency along y-axis.

Thus we plot the points (10,2),(15,14),(20,16),(25,20),(30,23),(35,27),(40,30)

We find that the two types of curves intersect of P from point L it is drawn on x-axis

The value of a profit corresponding to M is 17.5. Hence median is 17.5lakh