RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.6

RD Sharma Class 10 Solutions Chapter 7 Ex 7.6 PDF Free Download

Exercise 7.6 primarily discusses the relationship among mean, median and mode as well as constructing a cumulative frequency polygon(OGIVE). Problems in this exercise are well crafted to understand the two types of ogives and its applications. Students wanting to get an edge over these concepts can access the RD Sharma Solutions Class 10. Get the RD Sharma Solutions for Class 10 Maths Chapter 7 Statistics Exercise 7.6 PDF is provided below for further assistance when solving this exercise.

RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.6 Download PDF

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Access RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.6

1. Draw an ogive by less than the method for the following data:

No. of rooms 1 2 3 4 5 6 7 8 9 10
No. of houses 4 9 22 28 24 12 8 6 5 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 99
Less than or equal to 7 8 107
Less than or equal to 8 6 113
Less than or equal to 9 5 118
Less than or equal to 10 2 120

It’s required 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.

R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 1

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

Prepare a cumulative frequency distribution table by less than method and draw an ogive.

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 – 800 172 800 673
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.

R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 2

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:

Since the given frequency distribution is not continuous we will have to 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.

R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 3

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:

Doing for the less than method, we have

Profit per shop Mid-value No of shops:
Less than 0 0 0
Less than 0 – 50 25 12
Less than 50 – 100 75 18
Less than 100 – 150 125 27
Less than 150 – 200 175 20
Less than 200 – 250 225 17
Less than 250 – 300 275 6
Above 300 300 0

By plotting the respectively coordinates we can get the frequency polygon.

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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:

Firstly, we prepare the cumulative frequency table by less than method as given below:

Daily income Cumulative frequency
Less than 120 12
Less than 140 26
Less than 160 34
Less than 180 40
Less than 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).

R D Sharma Solutions For Class 10 Maths Chapter 7 Statistics ex 7.6 - 5

Also, access other exercise solutions of RD Sharma Class 10 Maths Chapter 7 Statistics

Exercise 7.1 Solutions

Exercise 7.2 Solutions

Exercise 7.3 Solutions

Exercise 7.4 Solutions

Exercise 7.5 Solutions

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