# MCQs for Class 10 Maths Chapter 14 Statistics

MCQs for Class 10 Maths **Chapter 14 Statistics.**: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

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# Class 10 MCQ Maths Chapter 14 Statistics

1. If x1, x2, x3,….., xn are the observations of a given data. Then the mean of the observations will be:

(a)Sum of observations/Total number of observations

(b)Total number of observations/Sum of observations

(c)Sum of observations+Total number of observations

(d)None of the above

Answer: (a)Sum of observations/Total number of observations

2. While computing mean of the grouped data, we assume that the frequencies are:

(a) evenly distributed over all the classes

(b) centered at the class marks of the classes

(c) centered at the upper limits of the classes

(d) centered at the lower limits of the classes

Answer: (b) centered at the class marks of the classes

3. Cumulative frequency curve is also called

(a) histogram

(b) ogive

(c) bar graph

(d) median

Answer: (b) ogive

4. One of the methods for determining mode is

(a) Mode = 2 Median -3 Mean

(b) Mode = 3 Median – 2 Mean

(c) Mode = 2 Mean – 3 Median

(d) Mode = 3 Mean – 2 Median

Answer: (b) Mode = 3 Median – 2 Mean

5. The abscissa of the point of intersection of both types (less than & more than) of cumulative frequency curves help in finding

(a) Mean

(b) Median

(c) Mode

(d) None of these

Answer: (b) Median

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6. Construction of a cumulative frequency table is useful determining the

(a) mean

(b) mode

(c) medien

(d) all of the above

Answer: (c) medien

7. If the mean of frequency distribution is 7.5 and ∑fi xi = 120 + 3k, ∑fi = 30, then k is equal to:

(a)40

(b)35

(c)50

(d)45

Answer: (b)35

8. For the following distribution,

Class | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 |

Frequency | 10 | 15 | 12 | 20 | 9 |

The sum of lower limits of median class and modal class is:

(a) 15

(b) 25

(c) 30

(d) 35

Answer: (b) 25

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9. The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

(a) is increased by 2

(b) is decreased by 2

(c) is two times of the original number

(d) Remains the same as that of the original set.

Answer: (d) Remains the same as that of the original set.

10. Mode is the

(a) middle most frequent value

(b) least frequent value

(c) maximum frequent value

(d) none of these

Answer: (c) maximum frequent value

11. The mean of the following data 12, 22, 32,…….n2 is –

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

(b) n(n – 1)(2n+1)/6

(c) n(n+1)(2n – 1)/6

(d) n(n – 1)(2n – 1)/6

Answer: (a) (n+1)(2n+1)/6

12. What should come in the blank? Mode= (…………..) –2 (mean)

(a)3 (median)

(b)4 (median)

(c)2 (median)

(d)5 (median)

Answer: (a)3 (median)

13. The mode and mean is given by 7 and 8, respectively. Then the median is:

(a)1/13

(b)13/3

(c)23/3

(d)33

Answer: (c)23/3

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14. If the arithmetic mean of x, x + 3, x + 6, x + 9 and x + 12 is 10, then x = ?

(a) 1

(b) 2

(c) 6

(d) 4

Answer: (d) 4

15. Mode and mean of a data are 12k and 15A. Median of the data is

(a) 12k

(b) 14k

(c) 15k

(d) 16k

Answer: (b) 14k

16. The algebraic sum of the deviations of a frequency distribution from its mean is always,

(a) greater than zero

(b) less than zero

(c) zero

(d) a non-zero number

Answer: (c) zero

17. The class mark of the class 15.5 – 20.5

(a) 15.5

(b) 20.5

(c) 18

(d) 5

Answer: (c) 18

18. The mean of the data: 4, 10, 5, 9, 12 is;

(a)8

(b)10

(c)9

(d)15

Answer: (a)8

19. If the mean of first n natural numbers is 5n/9, then n =?

(a) 6

(b) 7

(c) 9

(d) 10

Answer: (c) 9

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20. Mean of n numbers x1, x2, … xn is m. If xn is replaced by x, then new mean is

(a) m – xn + x

(b) nm−xn+x/n

(c) (n−1)m+x/n

(d) m−xn+x/n

Answer: (b) nm−xn+x/n

21. While computing mean of grouped data, we assume that the frequencies are

(a) centred at the upper limits of the classes

(b) centred at the lower limits of the classes

(c) centred at the classmarks of the classes

(d) evenly distributed over all the classes

Answer: (c) centred at the classmarks of the classes

22. If there are two class intervals 10-20 and 20-30, then in which interval will 20 fall?

(a) 10-20

(b) 20-30

(c) In both, 10-20 and 20-30

(d) Neither in 10-20 nor 20-30\

Answer: (b) 20-30

23. The median of the data 13, 15, 16, 17, 19, 20 is:

(a)30/2

(b)31/2

(c)33/2

(d)35/2

Answer: (c)33/2

24. If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increases by:

(a) 2

(b) 1.5

(c) 1

(d) 0.5

Answer: (d) 0.5

25. 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, 50 respectively. The correct mean is

(a) 48

(b) 49

(c) 50

(d) 60

Answer: (c) 50

26. Construction of a cumulative frequency table is useful in determining the

(a) mean

(b) median

(c) mode

(d) none of these

Answer: (c) mode

27. The mean and the median of a distribution are 45.9 and 46 respectively. The mode will be

(a) 45

(b) 47

(c) 48

(d) 46.2

Answer: (d) 46.2

28. If the mean of first n natural numbers is 3n/5, then the value of n is:

(a)3

(b)4

(c)5

(d)6

Answer: (c)5

29. The Median when it is given that mode and mean are 8 and 9 respectively, is:

(a) 8.57

(b) 8.67

(c) 8.97

(d) 9.24

Answer: (b) 8.67

30. Which of the following can not be determined graphically?

(a) Mean

(b) Median

(c) Mode

(d) None of these

Answer: (a) Mean

31. A batsman in his 12th innings makes a score of 63 runs and thereby increases his average score by 2. His average score after 12th innings is

(a) 51

(b) 45

(c) 41

(d) 60

Answer: (c) 41

32. If AM of a, a+3, a+6, a+9 and a+12 is 10, then a is equal to;

(a)1

(b)2

(c)3

(d)4

Answer: (d)4

33. The mean of the marks obtained by 7 students in a group is 226. If the marks obtained by six of them are 340, 180, 260, 56, 275, 307, then the marks obtained by the seventh student are

(a) 200

(b) 125

(c) 174

(d) 164

Answer: (d) 164

34. The class interval of a given observation is 10 to 15, then the classmark for this interval will be:

(a)11.5

(b)12.5

(c)12

(d)14

Answer: (b)12.5

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35. If median of 20 observations is 50 and mode is also 50, then the mean is

(a) 45

(b) 55

(c) 50

(d) 49

Answer: (c) 50

36. If the sum of frequencies is 24, then the value of x in the observation: x, 5,6,1,2, will be;

(a)4

(b)6

(c)8

(d)10

Answer: (d)10

37. The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is

(a) 28

(b) 29

(c) 30

(d) 31

Answer: (b) 29

38. The mean of following distribution is:

x_{i} | 11 | 14 | 17 | 20 |

f_{i} | 3 | 6 | 8 | 7 |

(a)15.6

(b)17

(c)14.8

(d)16.4

Answer: (d)16.4

39. The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is

(a) 28

(b) 29

(c) 31

(d) 30

Answer: (b) 29

40. The median of a distribution divides it into

(a) Three equal parts

(b) Does not divide into any parts.

(c) Two equal parts

(d) Four equal parts

Answer: (c) Two equal parts

41. The mean of the first 10 prime numbers is

(a) 12.9

(b) 1.29

(c) 129

(d) None of these

Answer: (a) 12.9

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42. The mean of the first 10 natural odd numbers is

(a) 9

(b) 10

(c) 11

(d) 12

Answer: (b) 10

43. The mean of all the factors of 24 is

(a) 7.5

(b) 24

(c) 7

(d) None of these

Answer: (a) 7.5

44. The class marks of the class 18-22 is

(a) 4

(b) 18

(c) 22

(d) 20

Answer: (d) 20

45. Mode is not affected by

(a) Maximum value

(b) Minimum value

(c) Extreme values

(d) All of the above

Answer: (d) All of the above

46. The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. The excluded number is

(a) 45

(b) 36

(c) 30

(d) 25

Answer: (b) 36

47. In a small scale industry, salaries of employees are given in the following distribution table:

Salary (in Rs.) | 4000 – 5000 | 5000-6000 | 6000-7000 | 7000-8000 | 8000-9000 | 9000-10000 |

Number of employees | 20 | 60 | 100 | 50 | 80 | 90 |

Then the mean salary of the employee is:

(a) Rs. 7350

(b) Rs. 7400

(c) Rs. 7450

(d) Rs. 7500

Answer: (c) Rs. 7450

48. For the following distribution

Marks 0-10 10-20 20-30 30-40 40-50

No. of students 3 9 13 10 5

the number of students who got marks less than 30 is

(a) 13

(b) 25

(c) 10

(d) 12

Answer: (b) 25

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49. The frequency of each class interval is centred around its ————-

(a) Lower limit

(b) Upper limit

(c) Mid-point

(d) None

Answer: (c) Mid-point

50. For the following distribution

Cl 0-5 5-10 10-15 15-20 20-25

f 10 15 12 20 9

the difference of the upper limit of the median class and the lower limit of the modal class is

(a) 0

(b) 5

(c) 10

(d) -5

Answer: (a) 0

51. In a hospital, weights of new born babies were recorded, for one month. Data is as shown:

Weight of new born baby (in kg) | 1.4 – 1.8 | 1.8 – 2.2 | 2.2 – 2.6 | 2.6 – 3.0 |

No of babies | 3 | 15 | 6 | 1 |

Then the median weight is:

(a) 2kg

(b) 2.03kg

(c) 2.05 kg

(d) 2.08 kg

Answer: (c) 2.05 kg

52. For the following distribution

C.I. 0-5 6-11 12-17 18-23 24-29

f 26 20 30 16 22

the upper limit of the median class is

(a) 18.5

(b) 18

(c) 17.5

(d) 17

Answer: (c) 17.5

53. The ——— of observations is the sum of the values of all the observations divided by the total number of observations.

(a) Mean or Average

(b) Median

(c) Mode

(d) none

Answer: (a) Mean or Average

54. For one term, absentee record of students is given below. If mean is 15.5, then the missing frequencies x and y are:

Number of days | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | TOTAL |

Total Number of students | 15 | 16 | x | 8 | y | 8 | 6 | 4 | 70 |

(a) x = 4 and y = 3

(b) x = 7 and y = 7

(c) x = 3 and y = 4

(d) x = 7 and y = 6

Answer: (d) x = 7 and y = 6

55. For the following distribution

C.I. 0-10 10-20 20-30 30-40 40-50

f 20 30 24 40 18

the sum of lower limits of the modal class and the median class is

(a) 20

(b) 30

(c) 40

(d) 50

Answer: (d) 50

56. Half of (upper class limit + lower class limit) is —————-

(a) Class interval

(b) Class mark

(c) Class value

(d) None

Answer: (b) Class mark

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57. Pocket expenses of a class in a college are shown in the following frequency distribution:

Pocket expenses | 0-200 | 200-400 | 400-600 | 600-800 | 800-1000 | 1000-1200 | 1200-1400 |

Number of students | 33 | 74 | 170 | 88 | 76 | 44 | 25 |

Then the median for the above data is:

(a) 485.07

(b) 486.01

(c) 487.06

(d) 489.03

Answer: (c) 487.06

58. For the following distribution

Marks No. of students

Less than 20 4

Less than 40 12

Less than 60 25

Less than 80 56

Less than 100 74

Less than 120 80

the modal class is

(a) 20 – 40

(b) 40 – 60

(c) 60 – 80

(d) 80 -100

Answer: (c) 60 – 80

59. In a hospital, weights of new born babies were recorded, for one month. Data is as shown:

Weight of new born baby (in kg) | 1.4 – 1.8 | 1.8 – 2.2 | 2.2 – 2.6 | 2.6 – 3.0 |

No of babies | 3 | 15 | 6 | 1 |

Then the median weight is:

(a) 2kg

(b) 2.03kg

(c) 2.05 kg

(d) 2.08 kg

Answer: (c) 2.05 kg

60. Mode is the

(a) middle most frequent value

(b) least frequent value

(c) maximum frequent value

(d) none of these

Answer: (c) maximum frequent value

61. In the given data:

C.I. | f |

65-85 | 4 |

85 – 105 | 5 |

105 – 125 | 13 |

125 – 145 | 20 |

145 – 165 | 14 |

165 – 185 | 7 |

185 – 205 | 4 |

the difference of the upper limit of the median class and the lower limit of the modal class is

(a) 38

(b) 20

(c) 19

(d) 0

Answer: (b) 20

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62. For the following distribution

Marks obtained | No. of students |

More than or equal to 0 | 63 |

More than or equal to 10 | 58 |

More than or equal to 20 | 55 |

More than or equal to 30 | 51 |

More than or equal to 40 | 48 |

More than or equal to 50 | 42 |

the frequency of the class 20-30 is

(a) 35

(b) 4

(c) 48

(d) 51

Answer: (b) 4

63. A ——- is that value among the observations which occurs most often.

(a) Mean

(b) Median

(c) Mode

(d) none

Answer: (c) Mode

64. The ——– is the most frequently used measure of central tendency.

(a) Mean

(b) Median

(c) Mode

(d) none

Answer: (a) Mean

65. Fill in the blanks:

3 Median = Mode + ————

(a)Mean

(b)2 Mean

(c) 3 Mean

(d) None

Answer: (b)2 Mean

66. The ——- of a class is the frequency obtained by adding the frequencies of all the classes preceding the given class.

(a) added frequency

(b) cumulative frequency

(c) frequency polygon

(d) None

Answer: (b) cumulative frequency

67. The ———- of grouped data can be obtained graphically as the x coordinate of the point of intersection of the two ogives for the data.

(a) Mean

(b) Median

(c) Mode

(d) none

Answer: (b) Median

68. is not a measure of central tendency of a statistical data.

(a) Mean

(b) Range

(c) Mode

(d) None

Answer: (b) Range

69. —- cannot be determined graphically.

(a) Mean

(b) Median

(c) Mode

(d) None

Answer: (a) Mean

70. Mode is the value of the variable which has ——————-

(a) Minimum frequency

(b) Maximum frequency

(c)no frequency

(d) none

Answer: (b) Maximum frequency

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71. Cumulative frequency curve is also known as ————

(a) Ogives

(b) Frequency curve

(c) Frequency polygon

(d) None

Answer: (a) Ogives

72. The class marks of the class 10 -20 is ————–

(a) 10

(b) 15

(c) 20

(d) None

Answer: (b) 15

73. If the mean and median of a data are 18 and 16 respectively their mode is ———–

(a) 10

(b) 12

(c) 14

(d) None

Answer: (b) 12

74. While drawing an ogive, cumulative frequencies are marked on ——– axis.

(a) x axis

(b) y axis

(c) none of these.

(d) None

Answer: (b) y axis

75. In the given data:

C.I | Frequency |

65-85 | 4 |

85 – 105 | 5 |

105 – 125 | 13 |

125 – 145 | 20 |

145 – 165 | 14 |

165 – 185 | 7 |

185 – 205 | 4 |

the difference of the upper limit of the median class and the lower limit of the modal class is

(a) 38

(b) 20

(c) 19

(d) 0

Answer: (b) 20

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