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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.
|
xi |
5 | 10 | 15 | 20 | 25 |
| fi | 7 | 4 | 6 | 3 | 5 |
Find the mean deviation about the mean for the data
| xi | 10 | 30 | 50 | 70 | 90 |
| fi | 4 | 24 | 28 | 16 | 8 |
Find the mean deviation about the median for the data.
|
xi |
5 |
7 |
9 |
10 |
12 |
15 |
|
fi |
8 |
6 |
2 |
2 |
2 |
6 |
Find the mean deviation about the median for the data
|
xi |
15 |
21 |
27 |
30 |
35 |
|
fi |
3 |
5 |
6 |
7 |
8 |
Find the mean deviation about the mean for the 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 |
Find the mean deviation about the mean for the data
|
Height in cms |
Number of boys |
|
95-105 |
9 |
|
105-115 |
13 |
|
115-125 |
26 |
|
125-135 |
30 |
|
135-145 |
12 |
|
145-155 |
10 |
Find the mean deviation about median for the following data:
|
Marks |
Number of girls |
|
0-10 |
6 |
|
10-20 |
8 |
|
20-30 |
14 |
|
30-40 |
16 |
|
40-50 |
4 |
|
50-60 |
2 |
Calculate the mean deviation about median age for the age distribution of 100 persons given below:
|
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 |
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 short-cut method.
|
xi |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
|
fi |
2 |
1 |
12 |
29 |
25 |
12 |
10 |
4 |
5 |
Find the mean and variance for the following 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 |
Find 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 |
Find the mean, variance and standard deviation using short-cut method
|
Height in cms |
No. 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 |
The diameters of circles (in mm) drawn in a design are given below:
|
Diameters |
No. of children |
|
33-36 |
15 |
|
37-40 |
17 |
|
41-44 |
21 |
|
45-48 |
22 |
|
49-52 |
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 |
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 |
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_(i-1)^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 σ2 is the variance of n observations x1, x2 … xn. Prove that the mean and variance of the observations ax1, ax2, ax3 …axn are `abarx` and a2 σ2, 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, step-by-step 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.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
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.
Using NCERT Class 11 Mathematics solutions Statistics exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Class 11 Mathematics students prefer NCERT Textbook Solutions to score more in exams.
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