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 |
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1
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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
Q2. Calculate 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?