# NCERT solutions for Class 11 Mathematics chapter 15 - Statistics [Latest edition]

## Solutions for Chapter 15: Statistics

Below listed, you can find solutions for Chapter 15 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

Exercise 15.1Exercise 15.2Exercise 15.3Miscellaneous Exercise
Exercise 15.1 [Pages 360 - 361]

### NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.1 [Pages 360 - 361]

Exercise 15.1 | Q 1 | Page 360

Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

Exercise 15.1 | Q 2 | Page 360

Find the mean deviation about the mean for the data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Exercise 15.1 | Q 3 | Page 360

Find the mean deviation about the median for the data.

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

Exercise 15.1 | Q 4 | Page 360

Find the mean deviation about the median for the data

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

Exercise 15.1 | Q 5 | Page 360

Find the mean deviation about the mean for the data.

 xi 5 10 15 20 25 fi 7 4 6 3 5
Exercise 15.1 | Q 6 | Page 360

Find the mean deviation about the mean for the data

 xi 10 30 50 70 90 fi 4 24 28 16 8

Exercise 15.1 | Q 7 | Page 360

Find the mean deviation about the median for the data.

 xi 5 7 9 10 12 15 fi 8 6 2 2 2 6

Exercise 15.1 | Q 8 | Page 360

Find the mean deviation about the median for the data

 xi 15 21 27 30 35 fi 3 5 6 7 8
Exercise 15.1 | Q 9 | Page 361

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
Exercise 15.1 | Q 10 | Page 361

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
Exercise 15.1 | Q 11 | Page 361

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
Exercise 15.1 | Q 12 | Page 361

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
Exercise 15.2 [Pages 371 - 372]

### NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.2 [Pages 371 - 372]

Exercise 15.2 | Q 1 | Page 371

Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12

Exercise 15.2 | Q 2 | Page 371

Find the mean and variance for the first natural numbers

Exercise 15.2 | Q 3 | Page 371

Find the mean and variance for the first 10 multiples of 3

Exercise 15.2 | Q 4 | Page 371

Find the mean and variance for the data

 xi 6 10 14 18 24 28 30 fi 2 4 7 12 8 4 3
Exercise 15.2 | Q 5 | Page 371

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
Exercise 15.2 | Q 6 | Page 371

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

Exercise 15.2 | Q 7 | Page 371

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
Exercise 15.2 | Q 8 | Page 372

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
Exercise 15.2 | Q 9 | Page 372

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
Exercise 15.2 | Q 10 | Page 372

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
Exercise 15.3 [Pages 375 - 376]

### NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.3 [Pages 375 - 376]

Exercise 15.3 | Q 1 | Page 375

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
Exercise 15.3 | Q 2 | Page 375

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
Exercise 15.3 | Q 3 | Page 375

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?

Exercise 15.3 | Q 3 | Page 380

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

Exercise 15.3 | Q 4 | Page 376

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?

Exercise 15.3 | Q 5 | Page 376

The sum and sum of squares corresponding to length (in cm) and weight (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?

Miscellaneous Exercise [Page 380]

### NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Miscellaneous Exercise [Page 380]

Miscellaneous Exercise | Q 1 | 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.

Miscellaneous Exercise | Q 2 | Page 380

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.

Miscellaneous Exercise | Q 3. | Page 380

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.

Miscellaneous Exercise | Q 4 | Page 380

Given that  barx is the mean and σ2 is the variance of observations x1x2 … xn. Prove that the mean and variance of the observations ax1ax2ax3 …axare abarx and a2 σ2, respectively (a ≠ 0).

Miscellaneous Exercise | Q 5 | Page 380

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.

Miscellaneous Exercise | Q 6 | Page 380

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?

Miscellaneous Exercise | Q 7 | Page 380

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

Exercise 15.1Exercise 15.2Exercise 15.3Miscellaneous Exercise

## NCERT solutions for Class 11 Mathematics chapter 15 - Statistics

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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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