# MCQs for Mathematics Class 11 with Answers Chapter 15 Statistics

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Statistics with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

**Chapter 15 Statistics MCQ with Answers Class 11 Mathematics**

MCQ Questions Class 11 Mathematics Statistics with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. 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

A

**Question: For a certain frequency table which has been partly reproduced here, the arithmetic mean was found to be Rs.28.07**

**If the total number of workers is 75, then the missing frequencies are**(a) 14, 15

(b) 15, 14

(c) 13, 16

(d) 12, 17

## Answer

B

**Question: If a variable take values 0 1, , …, 2, n with frequencies**

**,where p+ q = 1, then the mean is**

(a) n p

(b) n q

(c) n (p +q)

(d) None of these

## Answer

A

**Question: Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20 and 50, respectively. The correct mean is**

(a) 48

(b) 82.5

(c) 50

(d) 80

## Answer

C

**Question: The mode of the following distribution is**

(a) 46.67

(b) 40

(c) 44.67

(d) 45

## Answer

A

**Question: The mean deviation from the median is**

(a) greater than the measured from any other value

(b) less than that measured from any other value

(c) equal to that measured from any other value

(d) maximum if all observations are positive

## Answer

B

**Question: The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is**

(a) n + 1/2

(b) 3n(n+1)/2(2n+1)

(c) (n+1)(2n+1)

(d) n(n+1/2)

## Answer

B

**Question: The mean deviation from the mean of the AP a, a+d, a+2d,… a+ 2nd, is**

(a) n(n+1)d

(b) n(n +)d/2n+1)

(c) n (n+1)d/2n

(d) n(n -1)d/2n+1

## Answer

B

**Question: The variance of 6, 8 ,10, 12, 14 is**

(a) 7

(b) 8

(c) 12

(d) 16

## Answer

B

**Question: Let s be the standard deviation of n observations. Each of the observations is multiplied by a constant c. Then, the standard deviation of the resulting number is**

(a) s

(b) c s

(c) s√ c

(d) None of these

## Answer

B

**Question: The mean of 5 observations is 4 and their variance is 5.2. If three If there observations are 1, 2 and 6, then the other two are**

(a) 2 and 9

(b) 3 and 8

(c) 4 and 7

(d) 5 and 6

## Answer

C

**Question: The sum and sum of squares corresponding to length x (in cm) and weight(y)(in g) of 50 plant products are given below**

**and** **Which is more varying, the length or weight?**

(a) weight

(b) length

(c) cannot be determined

(d) None of these

## Answer

A

**Question:**

## Answer

A

**Question: If MD is 12, the value of SD will be**

(a) 75

(b) 12

(c) 24

(d) None of these

## Answer

A

**Question: The mean and standard deviation of six observations are 8 and 4,respectively. If each observation is multiplied by 3, then find the mean and new standard deviation of the resulting observations.**

(a) 24, 12

(b) 24,144

(c) 24, 150

(d) 12, 12

## Answer

A

**Question: The arithmetic mean of an AP and the mean of first and last term of an AP are**

(a) equal

(b) unequal

(c) square of each other

(d) None of the above

## Answer

A

**Question: A statistical measure which cannot be determined graphically is**

(a) median

(b) mode

(c) harmonic mean

(d) mean

## Answer

C

**Question: The average of the squares of the numbers 0, 1, 2, 3, 4,…, n is**

(a) 1/2 n(n+1)

(b) 1/6 n (2n+1)

(c) 1/6(n+1) (2n+1)

(d) 1/6 n (n+1)

## Answer

B

**Question: The mean height of 25 male workers in a factory is 61 cm and the mean height of 35 female workers in the same factory is 58 cm. The combined mean height of 60 workers in the factory is**

(a) 59.25

(b) 59.5

(c) 59.75

(d) 58.75

## Answer

A

**Question: If the average of the numbers 148, 146, 144, 142, … in AP, be 125, then the total numbers in the series****will be**

(a) 18

(b) 24

(c) 30

(d) 48

## Answer

B

**Question: The AM of n numbers of a series is x̅. If the sum of first (n – 1 terms is k, then the nth number is x̅,**

(a)^{ X̅,}-k

(b) n x̅,- k

(c) x̅- n k

(d) n x̅- n k

## Answer

B

**Question:**

## Answer

D

**Question: Mean of 100 items is 49. It was discovered that three** **items which should have been 60, 70 and 80 were** **wrongly read as 40, 20 and 50, respectively. The** **correct mean is**

(a) 48

(b) 821/2

(c) 50

(d) 80

## Answer

C

**Question: The mean of the values of 1, 2, 3, …, n with** **respectively frequencies x, 2x, 3x,…,nx is**

(a) n/2

(b) 1/3(2 n +1)

(c) 1/6(2n+1)

(d) n/2

## Answer

B

**Question: The mean of n items is X̅,. If the first term is increased** **by 1, second by 2 and so on, then the new mean is**

(a) x̅+n

(b) x̅ + n/2

(c) x̅ + n+1/2

(d) None of these

## Answer

C

**Question: For a certain frequency table which has been partly** **reproduced here, the arithmetic mean was found to** **be Rs. 28.07**.

Income (in R,s.) | Number of workers |

15 | 8 |

20 | 12 |

25 | ? |

30 | 16 |

35 | ? |

40 | 10 |

**If the total number of workers is 75, then missing frequencies are respectively**

(a) 14, 15

(b) 15, 14

(c) 13, 16

(d) 12, 17

## Answer

B

**Question: The weighted AM of first n natural numbers whose weights are equal to the corresponding numbers is equal to**

(a) 2n+1

(b) 1/2 (2n+1)

(c) 1/3 (2n+1)

(d) 2n+1/6

## Answer

C

**Question. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.****The mean deviation about the mean for the given data is**

(a) 8.4

(b) 7.4

(c) 6.3

(d) 4

## Answer

D

**Question. The mean deviation about the median of the given frequency distribution is (in years)**

(a) 3.24

(b) 2.24

(c) 8.1

(d) 7.2

## Answer

A

**Question. Mean deviation about the median for the data****3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 is**

(a) 4.27

(b) 5.24

(c) 5.27

(d) 4.24

## Answer

C

**Question. The scores of a batsman in 10 innings are 48, 80, 58, 44, 52, 65, 73, 56, 64, 54, then the mean deviation from the median is**

(a) 7.6

(b) 8.6

(c) 9.6

(d) 10.1

## Answer

B

**Question** . Consider the following data

**Question** .**Then, the mean deviation about the median for the data is**

(a) 5

(b) 5.3

(c) 5.1

(d) 5.2

## Answer

C

**Question. 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

B

**Question. 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

C

**Question. Consider the numbers 1, 2, 3, 4, 5, 6, 7,****8, 9, and 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

D

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

(a) 6.5

(b) 2.87

(c) 3.87

(d) 8.25

## Answer

D

**Question. The mean deviation about the median for the data 34, 66, 30, 38, 44, 50, 40, 60, 42, 51 is**

(a) 8.7

(b) 7.7

(c) 87

(d) 77

## Answer

A

**Question** . Consider the following data

**Then, the mean deviation about the mean is**

(a) 20

(b) 10

(c) 30

(d) 15

## Answer

B

**Question. 6, 5, 5.25, 5.5, 4.75, 4.5, 6.25, 7.75, 9.****The mean deviation from the mean for the given data is**

(a) 1.1

(b) 2.1

(c) 4.1

(d) 5.1

## Answer

A

**Question. 6, 7, 10, 12, 13, 4, 8, 12****The variance for the given data is**

(a) 8.25

(b) 9.25

(c) 10.5

(d) 8.9

## Answer

B

**Question. The mean deviation about the mean for the given data is**

(a) 2.1

(b) 2.2

(c) 2.3

(d) 2.4

## Answer

C

**Question** . Consider the following data

**Then, the mean deviation about the median for the data is**

(a) 3.15

(b) 3.23

(c) 3.21

(d) 3.17

## Answer

B

**Question. Mean deviation about the median for the data****13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 is**

(a) 2.44

(b) 2.33

(c) 1.44

(d) 1.33

## Answer

B

**Question. Variance of the data 2, 4, 5, 6, 8, 17 is 23.33. Then, variance of 4, 8, 10, 12, 16, 34 will be**

(a) 23.33

(b) 25.33

(c) 46.66

(d) 48.66

## Answer

C

**Question. The mean deviation about the median for the data****32, 34, 36, 38, 40, 42, 44, 46, 48, 50 is**

(a) 4.5

(b) 4

(c) 5.5

(d) 5

## Answer

D

**Question. Find the variance of the following data**

(a) 13

(b) 18

(c) 19

(d) 20

## Answer

C

**Question. The mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12 respectively are**

(a) 9, 9.50

(b) 8, 8.50

(c) 9, 9.25

(d) 8, 8.25

## Answer

C

**Question** . **Find the variance of the following data**

**Question. 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

C

**Question. The mean deviation from the mean of the set of observations −1, 0 and 4 is**

(a) 3

(b) 1

(c) −2

(d) 2

## Answer

D

**Question. The standard deviation for the data 6, 7, 10, 12, 13, 4, 8, 12 is**

(a) 8.25

(b) 7.25

(c) 9.25

(d) 10.25

## Answer

C

**Question. Consider the following data****36, 72, 46, 42, 60, 45, 53, 46, 51, 49****Then, the mean deviation about the median for the data is**

(a) 6

(b) 8

(c) 7

(d) None of the above

## Answer

C

**Question. If mean and standard deviation of 100 items are 50 and 4 respectively, then the sum of all the item and the sum of the squares of item is**

(a) 5000, 251600

(b) 5000, 256100

(c) 4000, 215600

(d) 4000, 255600

## Answer

A

**Question. 45, 60, 62, 60, 50, 65, 58, 68, 44, 48 The variance for the given data is**

(a) 56.2

(b) 66.2

(c) 65.2

(d) 55

## Answer

B

**Question. variance for the data given distribution is**

(a) 16

(b) 15

(c) 11

(d) 17

## Answer

D

**Question. The standard deviation of data 6, 5, 9, 13, 12, 8 and 10 is**

(a) 52/7

(b) 52/7

(c) 6

(d) 6

## Answer

A

**Question** . For a group of 200 candidates, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53, respectively

**Answer the following questions on the basis of above information.**

**(i) Find the sum of correct scores.**

(a) 7991

(b) 8000

(c) 8550

(d) 6572

## Answer

A

**(ii) Find the correct mean.**

(a) 42.924

(b) 39.955

(c) 38.423

(d) 41.621

## Answer

B

**(iv) Find the correct variance.**

(a) 280.3

(b) 235.6

(c) 224.143

(d) 226.521

## Answer

C

**(v) Find the correct standard deviation.**

(a) 14.971

(b) 11.321

(c) 16.441

(d) 12.824

## Answer

A

**Question** . You are given some observations as 34, 66, 30, 38, 44, 50, 40, 60, 42, 51.**Based on these observations, answer the following questions.**

**(i) The mean of the given data is**

(a) 40.5

(b) 45.0

(c) 45.5

(d) 50.5

## Answer

C

**(ii) The mean deviation about the mean is**

(a) 10.0

(b) 9.5

(c) 9.1

(d) 9.0

## Answer

D

**(iii) The median of the given data is**

(a) 41

(b) 42

(c) 43

(d) 44

## Answer

C

**(iv) The mean deviation about the median is**

(a) 8.0

(b) 8.3

(c) 8.5

(d) 8.7

## Answer

D

**(v) The difference between mean deviation about the mean and mean deviation about the median is**

(a) 0.1

(b) 0.2

(c) 0.3

(d) 0.4

## Answer

C

**Question** . Consider the data**Based above information answer the following questions. **

**(iii) Total frequency of the given data is**

(a) 10

(b) 20

(c) 50

(d) 60

## Answer

C

**(iv) Median of the given data is**

(a) 28

(b) 20

(c) 18

(d) 8

## Answer

A

**(v) Mean deviation about median is**

(a) 10.16

(b) 15

(c) 9.16

(d) 8.5

## Answer

A

**Question. You are given the following grouped data.**

**Based on these data, answer the following questions.**

**(i) Mean of the grouped data is**

(a) 7.0

(b) 7.5

(c) 8.0

(d) 8.5

## Answer

B

**(ii) Mean deviation about the mean is**

(a) 2.1

(b) 2.2

(c) 2.3

(d) 2.4

## Answer

C

**(iii) The value of median is**

(a) 5

(b) 6

(c) 7

(d) 8

## Answer

C

**(iv) Mean deviation about the median is**

(a) 1.9

(b) 2.0

(c) 2.2

(d) 2.3

## Answer

A

**(v) The difference between mean and median is**

(a) 0.9

(b) 0.7

(c) 0.5

(d) 0.3

## Answer

A

We hope the above MCQ Questions Class 11 Mathematics Statistics with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Statistics is an important chapter in Class 11 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefits of class 11 students. Please go through these and let us know if you have any feedback in the comments section.