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Edited By Ravindra Pindel | Updated on Sep 12, 2022 04:21 PM IST

**NCERT Exemplar Class 11 Maths Solutions Chapter 15** includes solutions to questions of all types such as short answer questions, long answer questions, value-based questions, MCQ’s and HOTS. The solutions are given by experts in a simple manner and are solved step-by-step. If you who have doubts regarding the chapter Statistics, then refer to NCERT Exemplar Class 11 Maths chapter 15 solutions and follow the solutions for better understanding of the concept. Students can download the pdf for Class 11 Maths NCERT Exemplar Solutions Chapter 15 which consists of all the important questions. You can cover all the important topics and sub-topics using the NCERT Exemplar Class 11 Maths solutions chapter 15 PDF Download function. You can also get your queries solved by referring to the solutions solved step by step in an easily comprehensible format.**Also, check -** NCERT Class 11 Maths Solutions for Other Chapters

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Question:1

Find the mean deviation about the mean of the distribution:

Answer:

We have to find the mean deviation about the mean of the distribution in this question.

Let us make a table of the given data and fill up the other columns after calculations

Hence, mean deviation becomes=

Question:2

Find the mean deviation about the median of the following distribution:

Answer:

The data distribution is given in the question.

We have to find the mean deviation about the median of the distribution in this question.

Let us make a table of the given data and fill up the other columns after calculations

Hence, mean deviation becomes

Question:3

Answer:

Set of first n natural numbers when n is an odd number is given

We have to find the mean deviation about the mean

We know that first natural numbers are 1, 2, 3 ……. , n .

It is given that n is odd number.

So, mean is

Question:4

Answer:

Set of first n natural numbers when n is an even number is given

We have to find the mean deviation about the mean

We know that first natural numbers are 1, 2, 3 ……. , n .

It is given that n is an even number.

So, mean is

Question:9

Answer:

A frequency distribution table is given where variance =160. We have to find the value of A, where A is a positive number. Let us make a table from the given data and fill out the other columns after calculation

And we know that variance is

Question:10

For the frequency distribution:

Find the standard distribution.

Answer:

A frequency distribution table is given and we have to find the standard deviation

Let us make a table from the given data and fill out the other columns after calculation

Substituting the value from the above table

Question:11

Answer:

It is given that there are 60 students in a class. The frequency distribution of the marks obtained by the students in a test is also given.

We have to find the mean and standard deviation of the marks.

It is given that there are 60 students in the class, so

And we know that standard deviation is

Question:12

Answer:

The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. We have to find the overall standard deviation.

As per the given criteria. In the first set of samples number of sample bulbs ,

Question:13

Answer:

Mean and standard deviation of 100 items are 50 and 4 respectively

We have to find the sum of all items and the sum of the squares of the items.

As per the question, number of items n =100

Question:14

If for a distribution and the total number of item is 18, find the mean and standard deviation.

Answer:

Substituting the corresponding values we get

Thus the mean and standard deviation of given items are 5.17 and 1.54 respectively.

Question:15

Find the mean and variance of the frequency distribution given below:

Answer:

Frequency distribution is given. We have to find the mean and variance

Converting the ranges of x to groups the given table can be re written as

And, we know that variance is

Question:16

Calculate the mean deviation about the mean for the following frequency distribution:

Answer:

A frequency distribution table is given, and we have to find the mean deviation about the mean

Let us make a table from the given data and fill out the other columns after calculation

Question:17

Calculate the mean deviation from the median of the following data:

Answer:

A frequency distribution table is given and we have to find the mean deviation about the median

Let us make a table from the given data and fill out the other columns after calculation

Now here N=20, which is even

Here

Question:18

Determine the mean and standard deviation for the following distribution:

Answer:

A frequency distribution table is given and we have to find the mean and standard deviation

Let us make a table from the given data and fill out the other columns after calculation

And we know that standard deviation is

Question:19

Answer:

A frequency distribution table for the weights of coffee in 70 jars is given and we have to find the variance and standard deviation of the distribution.

Let us make a table from the given data and fill out the other columns after calculation

And we know that standard deviation is

Variance = 1.17

Question:20

Answer:

The first n terms of an A.P are given whose first term is a and common difference is d. We have to find mean and standard deviation.

The given AP in tabular form is as shown below,

Question:21

Answer:

The marks obtained, out of 100, by 2 students Ravi and Hashina in 10 tests are given

We have to find who is more intelligent and who is more consistent

The marks of Ravi taken separately as follows

Here we have assumed 45 as mean

And we know that the standard deviation can be written as,

Here as

And we know that the standard deviation can be written as,

Question:22

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively.

If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27

respectively.

We have to find the correct standard deviation

As per the given criteria, Number of observations, n=100

Mean of the given observations before correction,

But we know

Substituting the corresponding values, we get

Also given that standard deviation of the 100 observations is 10 before correction

Question:24

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

A. 2

B. 2.57

C. 3

D. 3.75

Answer:

Given data is 3,10, 10, 4, 7 ,10 ,5 . They are total 7.

Question:26

When tested, the lives (in hours) of 5 bulbs were noted as follows:

1357, 1090, 1666, 1494, 1623

The mean deviations (in hours) from their mean is

A. 178

B. 179

C. 220

D. 356

Answer:

Hence, mean deviation becomes

Question:27

Following are the marks obtained by 9 students in a mathematics test:

50, 69, 20, 33, 53, 39, 40, 65, 59

The mean deviation from the median is:

A. 9

B. 10.5

C. 12.67

D. 14.76

Answer:

Given that the marks obtained by 9 students in a mathematics test are 50, 69 , 20 ,33, 53, 39 ,40, 65, 59 As number of students =9 which is odd

Hence Mean deviation becomes

Question:28

The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is

A.

B.

C.

D.

Answer:

Given data can be written in table form as,

Question:30

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is

A. 50000

B. 250000

C. 252500

D. 255000

Answer:

As per the question

Number of observation, n =100

Question:31

Let a, b, c, d, e be the observations with mean m and standard deviation s.

The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is

A. s

B. ks

C. s + k

D.

Answer:

Given observations are a, b, c, d, e

So, the mean of the 5 observations is

And the standard deviation of the 5 observations is

Now we will find the mean and standard deviation of the observations a+k , b+k, c+k, d+k, e+k we get

So, the mean of these 5 observations is

Question:33

Let be n observations. where l and k are constants. If the mean of 's is 48 and their standard deviation is 12, the mean of ’s is 55 and standard deviation of ’s is 15, the values of l and k should be

A. l = 1.25, k = – 5

B. l = – 1.25, k = 5

C. l = 2.5, k = – 5

D. l = 2.5, k = 5

Answer:

Question:34

Standard deviations for first 10 natural numbers is

A. 5.5

B. 3.87

C. 2.97

D. 2.87

Answer:

Question:35

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is

A. 6.5

B. 2.87

C. 3.87

D. 8.25

Answer:

We know that the standard deviation of the first n natural numbers is

Now for first 10 natural numbers n=10

substituting this in the equation of standard deviation we get

Now when 1 is added to each numbers of 1 , 2, 3, 4, 5, 6,7 ,8 ,9, 10 ; we get new series as 1+1, 2+1, 3+1, 4+1, 5+1, 6+1, 7+1, 8+1, 9+1, 10+1

Now we know if standard deviation of x series is s, then standard deviation of k+x series is s,

So the S.D of 1+1, 2+1, 3+1, 4+1, 5+1, 6+1, 7+1, 8+1, 9+1, 10+1 series is also same as the S.D of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 series.

Now for variance we will square on both the sides

Question:36

Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is

A. 8.25

B. 6.5

C. 3.87

D. 2.87

Answer:

First 10 positive integers are 1,2, 3, 4, 5,6 ,7, 8,9, 10 On multiplying each number by

-1 we get-1, -2, -3, -4 , -5, -6, -7, -8, -9 , -10

On adding 1 to each of the number, we get 0, -1, -2, -3, -4, -5, -6, -7, -8, -9

Question:37

The following information relates to a sample of size 60:

The variance is

A. 6.63

B. 16

C. 22

D. 44

Answer:

Question:38

Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is

A. 0

B. 1

C. 1.5

D. 2.5

Answer:

Question:39

The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be

A. 81

B. 57

C. 36

D. 25

Answer:

Question:40

Fill in the blanks

Coefficient of variation =

Answer:

Standard Deviation

We know that the Coefficient of variation can be written as

Question:41

Answer:

Zero, less than Given x is mean of n values, then the sum of all n terms is denoted by

so difference of both these is laways equal to zero i.e.

And square of the above equation is also equal to zero, so

Now if "a" has the value other than x then

Question:42

Answer:

11

We know the square root of variance is standard deviation

Taking square root on both sides, we get

So, if the variance of a data is 121, then the Standard deviation of the data is 11.

Question:43

Answer:

Independent, dependent

Change of origin means some value has been added or subtracted in the observation. And we know the S.D does not change if any value is added or subtracted from the observations, So SD is independent of change in origin.

However, Standard deviation is only affected by a change in scale, that is, when some value is multiplied or divided to observations. Hence, the SD of any data is independent of any change in origin but dependent on any change of scale.

Question:44

Answer:

Minimum

The sum of the squares of the deviations of the values of the variable is minimum or least when taken about their arithmetic mean.

Question:45

Fill in the blanks

The mean deviation of the data is _______ when measured from the median.

Answer:

Least

Mean deviation is sum of all deviations of a set of a data about the data’s mean. In addition, it is widely believed that the median is usually between the mean and the mode. So, the mean deviation of the data is least when measured from the median.

Question:46

Answer:

Greater than or equal to

SD is the difference between square of deviation of data about mean and square of mean. In addition, mean deviation is sum of all deviations of a set of data about the data’s mean. Hence, the SD is greater than or equal to the mean deviation taken from the arithmetic mean.

· Central Tendency

· Mean

· Median

· Mode

· Measure of Dispersion

· Range

· Quartile deviation

· Mean deviation

· Standard deviation

· Mean deviation for grouped data

· Mean deviation for ungrouped data

· Variance

· Analysis of Frequency Deviation

By referring to NCERT Exemplar Class 11 Maths chapter 15 solutions students can easily gather the various concepts of Statistics. Statistics carries a significant number of marks according to the CBSE paper pattern and the students should concentrate on important concepts like standard deviation and mean deviation, as they are frequently asked in the examination.

The step-wise and straightforward format of the NCERT exemplar solutions for Class 11 Maths chapter 15 makes it easy for the students to understand the most complex concepts of Statistics in a quick and easygoing manner. The pdf is exclusively created by our experts for students who find the concepts of Statistics difficult.

Students can easily score marks in this chapter by thoroughly studying a few topics which are commonly asked in the final examinations. The students will understand the concept in the simplest way possible by going through the NCERT Exemplar Class 11 Maths solutions chapter 15 Statistics.

As most students tend to skip the entire chapter due to doubts in Statistics, our experts have formulated the NCERT Exemplar Class 11 Maths chapter 15 solutions in the most student-friendly manner.

Standard Deviation: Questions on Standard Deviation are frequently asked by the examiners. The students should go through the NCERT Exemplar Class 11 Maths chapter 15 solutions to solve all their doubts regarding standard deviation. The student should just follow the simple steps given in the solution and practice.

Mean Deviation: The students should not ignore solving the question of mean deviation as they are commonly asked in the exam. The students should memorize the formula for mean and standard deviation upon which the problem is based and solve the entire question by referring to the steps given in the Class 11 Maths NCERT Exemplar solutions chapter 15.

Mean, Median, Mode, and Range: These are the fundamental concepts of Statistics and can be asked in the examination for MCQ or short answer type questions.

**Check Chapter-Wise NCERT Solutions of Book**

Chapter-1 | |

Chapter-2 | |

Chapter-3 | |

Chapter-4 | |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | Statistics |

Chapter-16 |

**Read more NCERT Solution subject wise -**

- NCERT Solutions for Class 11 Maths
- NCERT Solutions for Class 11 Physics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Biology

**Also, read NCERT Notes subject wise -**

- NCERT Notes for Class 11 Maths
- NCERT Notes for Class 11 Physics
- NCERT Notes for Class 11 Chemistry
- NCERT Notes for Class 11 Biology

**Also Check NCERT Books and NCERT Syllabus here:**

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Download EBook1. Which are the important topics one should cover in Statistics?

Standard Deviation, Mean Deviation and Central Tendency are the important topics one should cover in Statistics.

2. Where can we download the Class 11 Maths NCERT Exemplar Solutions Chapter 15?

Students can get PDF by using the NCERT Exemplar Class 11 Maths solutions chapter 15 PDF Download function.

3. Are the solutions helpful for board examinations?

Yes, NCERT Exemplar Class 11 Maths solutions chapter 15 are helpful for board examinations.

4. Can these solutions be referred for cracking competitive examinations?

Yes, Class 11 Maths NCERT Exemplar solutions chapter 15 can be referred to when pursuing competitive examinations.

Sep 06, 2024

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