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# NCERT Solutions for Class 11 Maths Chapter 15 Statistics

Topics and Sub Topics in Class 11 Maths Chapter 15 Statistics:

 Section Name Topic Name 15 Statistics 15.1 Introduction 15.2 Measures of Dispersion 15.3 Range 15.4 Mean Deviation 15.5 Variance and Standard Deviation 15 .6 Analysis of Frequency Distributions

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### Class 11 Maths NCERT Solutions  – Miscellaneous Questions

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Exercise 15.1

Q1. Calculate the mean deviation about the mean for the given data

5, 8, 9, 10, 11, 13, 14, 18

Q2Calculate the mean deviation about the mean for the given data

39, 71, 49, 41, 43, 56, 64, 47, 55, 45

Q3. Calculate the mean deviation about the median for the given data:

13, 16, 11, 10, 11, 12, 17, 14, 13, 16, 18, 17

Q4. Calculate the mean deviation about the median for the given data:

36, 46, 60, 53, 51, 72, 42, 45, 46, 49

Q5. Calculate the mean deviation about the mean for the given data

 xi 5 10 15 20 25 fi 7 4 6 3 5

Q6. Calculate the mean deviation about the mean for the given data

 xi 10 10 15 20 25 fi 7 4 6 3 5

Q7. Calculate the mean deviation about the median for the given data

 xi 10 10 15 20 25 fi 7 4 6 3 5
 xi 5 7 9 10 12 15 fi 8 6 2 2 2 6

Q8. Calculate the mean deviation about the median for the given data

 xi 15 21 27 30 35 fi 3 5 6 7 8

Q9. Calculate the mean deviation about the mean for the given data:

 Income per day Number of persons 0 – 100 4 100 – 200 8 200 – 300 9 300 – 400 10 400 – 500 7 500 – 600 5 600 – 700 4 700 – 800 3

Q10. Calculate the mean deviation about the mean for the given data:

 Height in cm Number of boys 95 – 105 9 105 – 115 13 115 – 125 26 125 – 135 30 135 – 145 12 145 – 155 10

Q11. Calculate the mean deviation about the median for the given data:

 Marks Number of girls 0 – 10 6 10 – 20 8 20 – 30 14 30 – 40 16 40 – 50 4 50 – 60 2

Q12.  Calculate the mean deviation about the median for the given data:

 Age Number 16 – 20 5 21 – 25 6 26 – 30 12 31 – 35 14 36 – 40 26 41 – 45 12 46 – 50 16 51 – 55 9

Exercise 15.2

Q1. Calculate mean and variance for the given data 6, 7, 10, 12, 13, 4, 8, 12

Q2. Calculate the mean and variance for the first n natural numbers.

Q3. Calculate the mean and variance for the first 10 multiples of 3.

Q4. Calculate the mean and variance for the data

 xi 6 10 14 18 24 28 30 fi 2 4 7 12 8 4 3

Q5. Calculate the mean and variance for the data

 xi 92 93 97 98 102 104 109 fi 3 2 3 2 6 3 3

Q6. Calculate the mean and standard deviation using short-cut method.

 xi 60 61 62 63 64 65 66 67 68 fi 2 1 12 29 25 12 10 4 5

Q7. Calculate the mean and variance for the given frequency distribution.

 Classes 0 – 30 30 – 60 60 – 90 90 – 120 120 – 150 150 – 180 180 – 210 Frequencies 2 3 5 10 3 5 2

Q8. Calculate the mean and variance for the following frequency distribution.

 Classes 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequencies 5 8 15 16 6

Q9. Calculate the mean, variance and standard deviation using short – cut method:

 Height in cm Number of children 70 – 75 3 75 – 80 4 80 – 85 7 85 – 90 7 90 – 95 15 95 – 100 9 100 – 105 6 105 – 110 6 110 – 115 3

Q10. The diameters of circles (in mm) drawn in a design are given below:

 Diameters Number of Children 33 – 36 15 37 – 40 17 41 – 44 21 45 – 48 22 49 – 52 25

Exercise 15.3

Q1. From the data given below state which group is more variable, A or B

 Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7

Q2. From the prices of shares X and Y below, find out which is more stable in value.

 X 35 54 52 53 56 58 52 50 51 49 Y 108 107 105 105 106 107 104 103 104 101

Q3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

 Firm A Firm B No. of wage earners 586 648 Mean of monthly wages Rs. 5253 Rs. 5253 Variance of the distribution of wages 100 121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Q4. The following is the record of goals scored by team A in a football session:

 Number of goals scored 0 1 2 3 4 Number of matches 1 9 7 5 3

For the team B, mean number of goals scored per match was 2 with standard deviation 1.25 goals. Find which team may be considered more consistent?