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Chapters
Chapter 2: Relations and Functions
Chapter 3: Trigonometric Functions
Chapter 4: Principle of Mathematical Induction
Chapter 5: Complex Numbers and Quadratic Equations
Chapter 6: Linear Inequalities
Chapter 7: Permutations and Combinations
Chapter 8: Binomial Theorem
Chapter 9: Sequences and Series
Chapter 10: Straight Lines
Chapter 11: Conic Sections
Chapter 12: Introduction to Three Dimensional Geometry
Chapter 13: Limits and Derivatives
Chapter 14: Mathematical Reasoning
Chapter 15: Statistics
Chapter 16: Probability
Solutions for Chapter 15: Statistics
Below listed, you can find solutions for Chapter 15 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.
NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.1 [Pages 360  361]
Find the mean deviation about the mean for the data
4, 7, 8, 9, 10, 12, 13, 17
Find the mean deviation about the mean for the data
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Find the mean deviation about the median for the data.
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
Find the mean deviation about the median for the data
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Find the mean deviation about the mean for the data.
x_{i} 
5  10  15  20  25 
f_{i}  7  4  6  3  5 
Find the mean deviation about the mean for the data
x_{i}  10  30  50  70  90 
f_{i}  4  24  28  16  8 
Find the mean deviation about the median for the data.
x_{i} 
5 
7 
9 
10 
12 
15 
f_{i} 
8 
6 
2 
2 
2 
6 
Find the mean deviation about the median for the data
x_{i} 
15 
21 
27 
30 
35 
f_{i} 
3 
5 
6 
7 
8 
Find the mean deviation about the mean for the data.
Income per day 
Number of persons 
0100 
4 
100200 
8 
200300 
9 
300400 
10 
400500 
7 
500600 
5 
600700 
4 
700800 
3 
Find the mean deviation about the mean for the data
Height in cms 
Number of boys 
95105 
9 
105115 
13 
115125 
26 
125135 
30 
135145 
12 
145155 
10 
Find the mean deviation about median for the following data:
Marks 
Number of girls 
010 
6 
1020 
8 
2030 
14 
3040 
16 
4050 
4 
5060 
2 
Calculate the mean deviation about median age for the age distribution of 100 persons given below:
Age 
Number 
1620 
5 
2125 
6 
2630 
12 
3135 
14 
3640 
26 
4145 
12 
4650 
16 
5155 
9 
NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.2 [Pages 371  372]
Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12
Find the mean and variance for the first n natural numbers
Find the mean and variance for the first 10 multiples of 3
Find the mean and variance for the data
xi 
6 
10 
14 
18 
24 
28 
30 
fi 
2 
4 
7 
12 
8 
4 
3 
Find the mean and variance for the data
xi 
92 
93 
97 
98 
102 
104 
109 
f i 
3 
2 
3 
2 
6 
3 
3 
Find the mean and standard deviation using shortcut method.
x_{i} 
60 
61 
62 
63 
64 
65 
66 
67 
68 
f_{i} 
2 
1 
12 
29 
25 
12 
10 
4 
5 
Find the mean and variance for the following frequency distribution.
Classes 
030 
3060 
6090 
90120 
120150 
150180 
180210 
Frequencies 
2 
3 
5 
10 
3 
5 
2 
Find the mean and variance for the following frequency distribution.
Classes 
010 
1020 
2030 
3040 
4050 
Frequencies 
5 
8 
15 
16 
6 
Find the mean, variance and standard deviation using shortcut method
Height in cms 
No. of children 
7075 
3 
7580 
4 
8085 
7 
8590 
7 
9095 
15 
95100 
9 
100105 
6 
105110 
6 
110115 
3 
The diameters of circles (in mm) drawn in a design are given below:
Diameters 
No. of children 
3336 
15 
3740 
17 
4144 
21 
4548 
22 
4952 
25 
NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.3 [Pages 375  376]
From the data given below state which group is more variable, A or B?
Marks 
1020 
2030 
3040 
4050 
5060 
6070 
7080 
Group A 
9 
17 
32 
33 
40 
10 
9 
Group B 
10 
20 
30 
25 
43 
15 
7 
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 
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?
The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations
The following is the record of goals scored by team A in a football session:
No. of goals scored 
0 
1 
2 
3 
4 
No. of matches 
1 
9 
7 
5 
3 
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?
The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
`sum_(i1)^50 x_i = 212, sum_(i=1)^50 x_i^2 = 902.8, sum_(i=1)^50 y_i = 261, sum_(i = 1)^50 y_i^2 = 1457.6`
Which is more varying, the length or weight?
NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Miscellaneous Exercise [Page 380]
The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12 and 14. Find the remaining two observations.
The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
Given that `barx` is the mean and σ^{2} is the variance of n observations x_{1}, x_{2} … x_{n}. Prove that the mean and variance of the observations ax_{1}, ax_{2}, ax_{3} …ax_{n }are `abarx` and a^{2} σ^{2}, respectively (a ≠ 0).
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted.
(ii) If it is replaced by 12.
The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject 
Mathematics 
Physics 
Chemistry 
Mean 
42 
32 
40.9 
Standard deviation 
12 
15 
20 
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.
Solutions for Chapter 15: Statistics
NCERT solutions for Class 11 Mathematics chapter 15  Statistics
Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, stepbystep solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC 15 (Statistics) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Class 11 Mathematics chapter 15 Statistics are Central Tendency  Median, Measures of Dispersion, Concept of Range, Mean Deviation, Introduction of Variance and Standard Deviation, Standard Deviation, Standard Deviation of a Discrete Frequency Distribution, Standard Deviation of a Continuous Frequency Distribution, Shortcut Method to Find Variance and Standard Deviation, Introduction of Analysis of Frequency Distributions, Comparison of Two Frequency Distributions with Same Mean, Statistics Concept, Central Tendency  Mean, Measures of Dispersion  Quartile Deviation, Standard Deviation  by Short Cut Method, Concept of Mode.
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