RD SHARMA Solutions for Class 11-science Maths Chapter 32 - Statistics

Chapter 32 - Statistics Exercise Ex. 32.1

Question 1

Calculate the mean deviation on the following income groups of five and seven members from their medians:

 

I Income in Rs. 

II income in Rs. 

4000

3800

4200

4000

4400

4200

4600

4400

4800

4600

 

4800

 

5800

 

 

Solution 1

  

Note: Answer given in the book is incorrect.

Question 2

Solution 2

Question 3

Solution 3




Question 4

Solution 4




Question 5

Solution 5





Question 6

Solution 6




Question 7

Solution 7



Question 8

Solution 8

 

Question 9

Solution 9



Question 10

Solution 10


Question 11

Calculate the mean deviation about the mean of the following data:

(v) 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

Solution 11

Question 12

Solution 12

Question 13

Solution 13



Question 14

Solution 14










































Question 15

Solution 15



Question 16

Solution 16

Chapter 32 - Statistics Exercise Ex. 32.2

Question 1

Find the mean deviation from the mean for the following data:

Size:

1 3 5 7 9 11 13 15

Frequency:

3 3 4 14 7 4 3 4

 

 

Solution 1

  

Question 2

Find the mean deviation from the median for the following data:

xi

15 21 27 30

fi

 3 5 6 7

 

 

Solution 2

  

Note: Answer given in the book is incorrect.

 

Question 3



Solution 3

Question 4



Solution 4


Question 5

Solution 5

Question 6

Solution 6

Question 7


Solution 7


Question 8

Solution 8


Question 9

Solution 9

Question 10


Solution 10


Question 11

Solution 11

Chapter 32 - Statistics Exercise Ex. 32.3

Question 1

Calculate mean deviation about median age for the age distribution of 100 persons given below:

Age:

16-20

21-25

26-30

31-35

36-40

41-45

45-50

50-55

Number of persons

5

6

12

14

26

12

16

9

 

 

Solution 1

  

Question 2


Solution 2



Question 3


Solution 3


Question 4

Solution 4

Question 5

Solution 5


Question 6


Solution 6


Question 7


Solution 7


Question 8


Solution 8

Question 9

Solution 9

Question 10

Solution 10

Chapter 32 - Statistics Exercise Ex. 32.4

Question 1

Show that the two formulae for the standard deviation of ungrouped data

  

Solution 1

  

Question 2

Solution 2




Question 3

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

Solution 3




Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8
Solution 8
Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13


Question 14

Solution 14

Chapter 32 - Statistics Exercise Ex. 32.6

Question 1

Calculate mean, variance and standard deviation of the following frequency distribution:

 

Class:

0-10

10-20

20-30

30-40

40-50

50-60

Frequency:

11

29

18

4

5

3

 

Solution 1

  

Question 2

Find the mean and variance of frequency distribution given below:

xi:

1 x <3

3  x<5

5 x<7

7 x<9

Fi:

6

4

5

1

 

Solution 2

  

Note: Answer given in the book is incorrect. 

 

Question 3


Solution 3


Question 4


Solution 4


Question 5


Solution 5


Question 6

Solution 6

Question 7

Calculate the Mean, median and Standard Deviation of the following distribution:

Solution 7

Question 8

Solution 8

Question 9

Mean and standard deviation of 100 observation were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

Solution 9

Question 10

While calculating the mean and variance of 10 readings , a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Solution 10

Chapter 32 - Statistics Exercise Ex. 32.7

Question 1

Life of bulbs product by two factories A and B are given below:

Length of life

(in hours):

Factory A:

550-650 650-750 750-850 850-950 950-1050

(Number of bulbs)

Factor B:

10   22 52 20 16

(Number of bulbs)

8  60 24 15 12

 

The bulbs of which factory are more consistent from the point of view of length of life?

Solution 1

  

Question 2

Following are mark obtained, out of 100, by two students Ravi and Hashina in 10 tests:

Ravi:

25 50 45 30 70 42 36 48 35 60

Hashina:

10 70 50 20 95 55 42 60 48 80

 

Who is more intelligent and who is more consistent?

Solution 2

  

Question 3

Solution 3

We observe that the average monthly wages in both firms is same i.e. Rs. 2500. Therefore the plant with greater variance will have greater variability. Thus plant B has greater variability in individual wages. 

Question 4


Solution 4

Question 5

Solution 5

Question 6


Solution 6


Question 7


Solution 7

Question 8


Solution 8

Question 9


Solution 9

Question 10


Solution 10




Question 11


Solution 11


Question 12


Solution 12




Chapter 32 - Statistics Exercise Ex. 32.5

Question 1


Solution 1


Question 2

Solution 2



Question 3

F i n d space t h e space m e a n comma space a n d space t h e space s tan d a r d space d e v i a t i o n space f o r space t h e space f o l l o w i n g space d a t a :

(i)

(ii)

Solution 3

Question 4

(ii)



Solution 4

Chapter 32 - Statistics Exercise Ex. 32VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

W e space k n o w space t h a t space i f space y subscript i equals a x subscript i plus b comma space t h e n space v a r left parenthesis Y right parenthesis equals a squared left square bracket v a r left parenthesis X right parenthesis right square bracket
H e r e comma space Y equals fraction numerator a X plus b over denominator c end fraction equals a over c X plus b over c
T h e r e f o r e comma space v a r left parenthesis Y right parenthesis equals space a squared over c squared left square bracket v a r left parenthesis X right parenthesis right square bracket equals fraction numerator a squared sigma squared over denominator c squared end fraction
S. D. equals open vertical bar a over c close vertical bar sigma

Question 5

Solution 5

Question 6

Solution 6

New SD is open vertical bar a close vertical bar sigma

Question 7

Solution 7

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