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# Chapter 7: Statistics Exercise – 7.6

### Question: 1

Draw an Ogive by less than the method for the following data:

 No. of rooms No. of houses 1 4 2 9 3 22 4 28 5 24 6 12 7 8 8 6 9 5 10 2

### Solution:

 No. of rooms No. of houses Cumulative Frequency Less than or equal to 1 4 4 Less than or equal to 2 9 13 Less than or equal to 3 22 35 Less than or equal to 4 28 63 Less than or equal to 5 24 87 Less than or equal to 6 12 97 Less than or equal to 7 8 107 Less than or equal to 8 6 113 Less than or equal to 9 5 119 Less than or equal to 10 2 120

We need to plot the points (1, 4), (2, 3), (3, 35), (4, 63), (5, 87), (6, 99), (7, 107), (8, 113), (9, 118), (10, 120), by taking upper class limit over the x-axis and cumulative frequency over the y-axis. ### Question: 2

The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

 Marks No. of Students 600 – 640 16 640 – 680 45 680 – 720 156 720 – 760 284 760 – 800 172 800 – 840 59 840 – 880 18

### Solution:

 Marks No. of Students Marks Less than Cumulative Frequency 600 – 640 16 640 16 640 – 680 45 680 61 680 – 720 156 720 217 720 – 760 284 760 501 760 – 800 172 800 693 800 – 840 59 840 732 840 – 880 18 880 750

Plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732), (880, 750) by taking upper class limit over the x-axis and cumulative frequency over the y-axis. ### Question: 3

Draw an Ogive to represent the following frequency distribution:

 Class-interval 0 – 4 5 – 9 10 – 14 15 – 19 20 – 24 No. of students 2 6 10 5 3

### Solution:

The given frequency distribution is not continuous, so we will first make it continuous and then prepare the cumulative frequency:

 Class-interval No. of Students Less than Cumulative frequency 0.5 – 4.5 2 4.5 2 4.5 – 9.5 6 9.5 8 9.5 – 14.5 10 14.5 18 14.5 – 19.5 5 19.5 23 19.5 – 24.5 3 24.5 26

Plot the points (4.5, 2), (9.5, 8), (14.5, 18), (19.5, 23), (24.5,26) by taking the upper class limit over the x-axis and cumulative frequency over the y-axis. ### Question: 4

The monthly profits (in Rs) of 100 shops are distributed as follows:

 Profit per shop No of shops: 0 – 50 12 50 – 100 18 100 – 150 27 150 – 200 20 200 – 250 17 250 – 300 6

Draw the frequency polygon for it

### Solution:

We have

 Profit per shop Mid-value No of shops: Less than 0 0 0 Less than 0 – 60 25 12 Less than 60 – 120 75 18 Less than 120 – 180 125 27 Less than 180 – 240 175 20 Less than 240 – 300 225 17 Less than 300 – 360 275 6 Above 360 300 0 ### Question: 5

The following distribution gives the daily income of 50 workers of a factory:

 Daily income (in Rs): No of workers: 100 – 120 12 120 – 140 14 140 – 160 8 160 – 180 6 180 –  200 10

Convert the above distribution to a 'less than' type cumulative frequency distribution and draw its ogive.

### Solution:

We first prepare the cumulative frequency table by less than method as given below:

 Daily income Cumulative frequency <120 12 <140 26 <160 34 <180 40 <200 50

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. Thus we plot the point (120, 12), (140, 26), (160, 34), (180, 40), (200, 50). ### Question: 6

The following table gives production yield per hectare of wheat of 100 farms of a village:

 Production yield: No of farms: 50 – 55 2 55 – 60 8 60 – 65 12 65 – 70 24 70 – 75 38 75 – 80 16

Draw 'less than' ogive and 'more than' ogive

### Solution:

Less than method: Cumulative frequency table by less than method

 Production yield Number of farms Production yield more than Cumulative frequency 50 – 55 2 55 2 55 – 60 8 60 10 60 – 65 12 65 22 65 – 70 24 70 46 70 – 80 38 75 84 75 – 80 16 80 100

Now we mark on x-axis upper class limit, y-axis cumulative frequencies. We plot the point (50,100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16) ### Question: 7

During the medical check-up of 35 students of a class, their weight recorded as follows:

 Weight (in kg) No of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the verify the result my using the formula.

### Solution:

Less than method: It is given that On x-axis upper class limits. Y-axis cumulative frequency We plot the points (38, 0), (40, 3), (42, 5), (44, 9), (46, 4), (48, 28), (50, 32), (52, 35).

More than method: cumulative frequency

 Weight No. of students Weight more than Cumulative frequency 38 – 40 3 38 34 40 – 42 2 40 32 42 – 44 4 42 30 44 – 46 5 44 26 46 – 48 14 46 21 48 – 50 4 48 7 50 – 52 3 50 3

x – axis lower class limits on y-axis cf We plot the points (38, 35), (40, 32), (42, 30), (44, 26), (46, 26), (48, 7), (50,3). ### Question: 8

The following table shows the height of trees:

 Height No. of trees Less than  7 26 Less than  14 27 Less than  21 92 Less than  28 134 Less than  35 216 Less than  42 287 Less than  49 341 Less than  56 360

Draw 'less than' ogive and 'more than' ogive

### Solution:

By less than method

 Height No. of trees Less than  7 26 Less than  14 27 Less than  21 92 Less than  28 134 Less than  35 216 Less than  42 287 Less than  49 341 Less than  56 360

Plot the points (7, 26), (14, 57), (21, 92), (28, 134), (35, 216), (42, 287), (49, 341), (56, 360) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.

By more than method:

 Height No. of trees Height more than C.F. 0 – 7 26 0 360 7 – 14 27 5 334 14 – 21 92 10 303 21 – 28 134 15 268 28 – 35 216 20 226 35 – 42 287 25 144 42 – 49 341 30 73 49 – 56 360 35 19 ### Question: 9

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.

### Solution:

More than method:

 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

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 Profits 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 17.5 lakh 