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# NCERT solutions for Class 11 Mathematics chapter 15 - Statistics

## Mathematics Textbook for Class 11

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## Chapter 15: Statistics

#### Chapter 15: Statistics solutions [Pages 360 - 361]

Q 1 | Page 360

Find the mean deviation about the mean for the data

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

Q 2 | Page 360

Find the mean deviation about the mean for the data

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

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

Q 4 | Page 360

Find the mean deviation about the median for the data

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

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
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

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

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
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
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
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
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

#### Chapter 15: Statistics solutions [Pages 371 - 372]

Q 1 | Page 371

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

Q 2 | Page 371

Find the mean and variance for the first natural numbers

Q 3 | Page 371

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

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
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
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

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
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
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
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

#### Chapter 15: Statistics solutions [Pages 375 - 380]

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
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
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

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?

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?

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?

#### Chapter 15: Statistics solutions [Page 380]

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.

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.

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).

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.

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?

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.

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

NCERT solutions for Class 11 Maths chapter 15 (Statistics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 15 Statistics are Standard Deviation - by Short Cut Method, Measures of Dispersion - Quartile Deviation, Central Tendency - Mode, Central Tendency - Mean, Statistics Concept, Comparison of Two Frequency Distributions with Same Mean, Introduction of Analysis of Frequency Distributions, Shortcut Method to Find Variance and Standard Deviation, Standard Deviation of a Continuous Frequency Distribution, Standard Deviation of a Discrete Frequency Distribution, Standard Deviation, Introduction of Variance and Standard Deviation, Mean Deviation, Concept of Range, Measures of Dispersion, Central Tendency - Median.

Using NCERT Class 11 solutions Statistics exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 15 Statistics Class 11 extra questions for Maths and can use shaalaa.com to keep it handy for your exam preparation

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