MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 1,590 off
USE CODE: SELF10

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.

Graph of Ogive

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.

Graph of Ogive

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.

Graph of Ogive

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

Graph of Ogive

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).

Graph of Ogive

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)

Graph of Ogive

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).

Graph of Ogive

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

Graph of Ogive

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

Graph of Ogive

Get Extra Rs. 1,590 off

COUPON CODE: SELF10


Course Features

  • 728 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution