RD PUBLIC SCHOOL BETUL

CLASS 10TH

MATH QUESTION

Statistics

Objective type questions (1 mark)

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

1. Mean

2. Mode

3. Median

4. All of the above .K

2. The abscissa of the point of interaction of the ‘less than type’ and of the ‘more than type’

cumulative frequency curve of grouped data gives

1. Mode

2. Median

3. Mean

4. All of the above .K

3. What should be the modal class

Number of

Marks students

Below

3

10

Below

12

20

Below

27

30

Below

57

40

Below

75

50

Below

80

60

1. 15-60

2. 30-40

3. 20-30

4. 10-20 .U

4. What should be the modal class

1 2 3 4 5

0

0 0 0 0 0

Clas -

- - - - -

ses 1

2 3 4 5 6

0

0 0 0 0 0

Fre

que 1 3 3

5 6 4

ncie 3 8 0 s

1. 10-20

2. 30-40

3. 40-50

4. 50-60 .U

5. What should be the frequency of 30-40 in this case

Marks obtained Number of students

More than or equal to 0 63 More than or

58

equal to 10

More than or

55

equal to 20

More than or

51

equal to 30

More than or

48

equal to 40

More than or

42

equal to 50

1. 51

2. 48

3. 4

4. 3 .U

6. What should come in the blank?

Mode= (…………..) –2 (mean)

1. 3 (median)

2. 4 (median)

3. 2 (median)

4. 5 (median) .K

7. What should be the modal class?

Classes Frequencies

0-10 12

10-20 16

20-30 17

30-40 13

40-50 11

50-60 19

1. 0-10

2. 10-20

3. 20-30

4. 50-60 .U

8. For a frequency distribution, mean, median and mode are connected by the relation

(a) mode = 3mean – 2median (b) mode = 2median – 3mean

(c) mode = 3median – 2mean (d) mode = 3median + 2mean .K

9. Which measure of central tendency is given by the x – coordinate of the point of

intersection of the more than ogive and less than ogive?

(a) mode (b) median (c) mean (d) all the above three measures .K

10. The class mark of a class interval is

(a) upper limit +lower limit (b) upper limit – lower limit

(c) 12 (upper limit + lower limit) (d) 12 (upper limit – lower limit) .K

11. Construction of cumulative frequency table is useful in determining the (a) mode

(b) median (c) mean (d) all the above three measures .K

12. For the following distribution

Marks Number of students

Below 10 3

Below 20 12

Below 30 27

Below 40 57

Below 50 75

Below 60 80 the

modal class is

(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 40 – 50 .U

13. For the following distribution

Marks Number of students

Below 10 3

Below 20 12

Below 30 27

Below 40 57

Below 50 75

Below 60 80 the

median class is

(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 40 – 50 .U

14. In a continuous frequency distribution, the median of the data is 24. If each item is

increased by 2, then the new median will be

(a) 24 (b) 26 (c) 12 (d) 48 .A

15. In a grouped frequency distribution, the mid values of the classes are used to measure

which of the following central tendency?

(a) mode (b) median (c) mean (d) all the above three measures .K

16. Which of the following is not a measure of central tendency of a statistical data? (a) mode

(b) median (c) mean (d) range .K

17. Weights of 40 eggs were recorded as given below:

Weights (in gms) 85 – 89 90 – 94 95 – 99 100 – 104 105- 109 No. of eggs 10 12 12 42 the lower

limit of the median class is

(a) 90 (b) 95 (c) 94.5 (d) 89.5 .U

18. The median class of the following distribution is

C.I 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

F 8 10 12 22 30 18

(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 40 – 50 .U

19. Weights of 40 eggs were recorded as given below:

Weights (in gms) 85 – 89 90 – 94 95 – 99 100 – 104 105- 109

No. of eggs 10 12 15 4 2

The lower limit of the modal class is

(a) 90 (b) 95 (c) 94.5 (d) 89.5 .U

20. The arithmetic mean of 12 observations is 7.5. If the arithmetic mean of 7 of these

observations is 6.5, the mean of the remaining observations is (a) 5.5 (b) 8.5 (c) 8.9 (d)

9.2 .U

21. In a continuous frequency distribution, the mean of the data is 25. If each item is increased

by 5, then the new median will be

(a) 25 (b) 30 (c) 20 (d) none of these .U

22. In a continuous frequency distribution with usual notations, if l = 32.5, f1 = 15, f0 = 12, f2 =

8 and h = 8, then the mode of the data is

(a) 32.5 (b) 33.5 (c) 33.9 (d) 34.9 .U

23. The arithmetic mean of the following frequency distribution is 25, then the value of p is C.I

0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 F 5 18 15 p 6

(a) 12 (b) 16 (c) 18 (d) 20 .U

24. If the mean of the following frequency distribution is 54, then the value of p is C.I 0 – 20 20

– 40 40 – 60 60 – 80 80 –100 F 7 p 10 9 13

(a) 12 (b) 16 (c) 18 (d) 11 .U

25. The mean of the following frequency distribution is C.I 0 – 10 10 – 20 20 – 30 30 – 40 40 –

50 F 12 16 6 7 9

(a) 12 (b) 16 (c) 22 (d) 20 .U

26. The mean of the following frequency distribution is C.I 0 – 10 10 – 20 20 – 30 30 – 40 40 –

50 F 7 8 12 13 10

(a) 12.2 (b) 16.2 (c) 22.2 (d) 27.2 .U

27. The median of the following frequency distribution is C.I 100 – 150 150 – 200 200 – 250

250 – 300 300 – 350 F 6 3 5 20 10

(a) 120 (b) 160 (c) 220 (d) 270 .U

28. The range of the data 14, 27, 29, 61, 45, 15, 9, 18 is (a)

61 (b) 52 (c) 47 (d) 53 .K

29. The class mark of the class 120 – 150 is (a) 120 (b) 130

(c) 135 (d) 150 .K

30. The class mark of a class is 10 and its class width is 6.

The lower limit of the class is

(a) 5 (b) 7 (c) 8 (d) 10 .K

31. In a frequency distribution, the class width is 4 and the lower limit of first class is 10. If

there are six classes, the upper limit of last class is (a) 22 (b) 26 (c) 30 (d) 34 .U

32. The class marks of a distribution are 15, 20, 25 ….45. The class corresponding to 45 is

(a) 12.5 – 17.5 (b) 22.5 – 27.5 (c) 42.5 – 47.5 (d) none of these .U

33. The number of students in which two classes are equal.

(a) VI and VIII (b) VI and VII (c) VII and VIII (d) none of these .K

34. The mean of first five prime numbers is (a) 5.0 (b) 4.5 (c) 5.6 (d)

6.5 .K

35. The mean of first ten multiples of 7 is

(a) 35.0 (b) 36.5 (c) 38.5 (d) 39.2 .K

36. The mean of x + 3, x – 2, x + 5, x + 7 and x + 72 is (a) x + 5 (b) x + 2 (c)

x + 3 (d) x + 7 .U

37. The mean of 10 observations is 42. If each observation in the data is

decreased by 12, the new mean of the data is

(a) 12 (b) 15 (c) 30 (d) 54 .U

38. The median of 10, 12, 14, 16, 18, 20 is (a) 12 (b) 14 (c) 15 (d)

16 .U

39. If the median of 12, 13, 16, x + 2, x + 4, 28, 30, 32 is 23, when x

+ 2, x + 4 lie between 16 and 30, then the value of x is

(a) 18 (b) 19 (c) 20 (d) 22 .U

40. If the mode of 12, 16, 19, 16, x, 12, 16, 19, 12 is 16, then the value of x is (a) 12 (b)

16 (c) 19 (d) 18 .U

41. The mean of the following data is x 5 10 15 20 25

f 3 5 8 3 1

(a) 12 (b) 13 (c) 13.5 (d) 13.6 .U

42. The mean of 10 numbers is 15 and that of another 20 number is 24 then the mean

of all 30 observations is

(a) 20 (b) 15 (c) 21 (d) 24 .A

43. Construction of cumulative frequency table is useful in determining the (a) Mean

(b) median (c) mode (d) all three .K

44. 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 the median class and the modal class is (a)

15 (b) 25 (c) 30 (d) 35 .U

45. Consider the following frequency distribution:

Class 0-9 10-19 20-29 30-39 40-49

Frequency 13 10 15 8 11

The upper limit of the median class is

(a) 29 (b) 29.5 (c) 30 (d) 19.5 .U

46. The abscissa of the point of intersection of the less than type and of the more than type

ogives gives its

(a) mean (b) median (c) mode (d) all three .A

47. For the following distribution: the modal class is Marks Below 10 Below 20 Below 30 Below

40 Below 50 No. of Students 8 17 32 62 80

(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 40 – 50 .U

48. From the following data of the marks obtained by students of class X Marks 0-10 10-20

2030 30-40 40-50 50-60 No. of Students 8 12 20 30 10 10 How many students, secured less

than 40 marks?

(a) 70 (b) 40 (c) 80 (d) 30 .U

49. The times in seconds taken by 150 athletics to run a 100m hurdle race are given as under:

Class 12.7-13 13-13.3 13.3-13.6 13.6-13.9 13.9-13.12 Frequency 5 6 10 55 41The number of

athletes who completed the race in less than 13.9 sec is (a) 21 (b) 55 (c) 41 (d) 76 .A

50. Consider the data:

Class 25-45 45-65 65-85 85-105 105-125 125-145

Frequency 4 5 12 20 14 11

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

(a) 0 (b) 19 (c) 20 (d) 38 .K

51. Consider the following distribution:

Marks above 0 above 10 above 20 above 30 above 40 Above 50

No. of Students 63 58 55 51 48 42

The frequency of the class 30 – 40 is

(a) 3 (b) 4 (c) 48 (d) 41 .S

Very short answer type questions (1 mark)

52. In figure the value of the median of the data using the graph of less than ogive and more

than ogive is

0

(a) 5 (b) 40 (c) 80 (d) 15 .K

53. Write the empirical relationship among the three measures of central tendency. K

54. What represents the abscissa of the point of intersection of more than type and of the

more than cumulative frequency of curves of a grouped data? K

55. A data has 35 observations arranged in ascending order. Find the observation which

represents the median. S

56. Which measures of central tendency can’t be found graphically? K

57. If mean = 20 , median = 30 find mode. U

58. If Mean = 20, mode = 29 find median. U

59. If mode = 40 and mean = 130 find median . U

60. If mode = 12, mean = 120 find median . U

61. If mean = 20, median = 28 find mode. U

62. Find the empirical relationship between the three measures of central tendencies. K

63. The relation connecting the measures of central tendencies is :

(a) mode = 2 median – 3 mean

(b) mode = 3 median – 2 mean

(c) mode = 2 median + 3 mean

(d) mode = 3 median + 2 mean .K

64. If the variance of a data is 12.25, then the standard deviation is

(a) 3.5 (b) 3 (c) 2.5 (d) 3.25 .U

66. What is the mean of 1st n natural numbers ? K

67. The mean of 9 observations is 60. If the mean of 1st 5 observation is 50 and that of last of 5

observations 45. Find the 6th observation. A

68. What is the average of 1st ten prime numbers ? U

69. What is the point of intersection of abscissa of more than type and less than type

cumulative frequency called? K

70. Consider the following frequency distribution of the height of 60 students of a class.

Find the sum of lower limit & upper limits of modal class .U

71. What is mode of a data if mean is 32 and median is 24. U

Short answer type questions (2 marks)

72. Convert the given cumulative frequency table into frequency distribution table .S

73. Write the following distribution as less than type cumulative frequency distribution. S

74. Find the median & modal class for the following distribution. U

75. Write the following distribution as less than type cumulative frequency distribution. S

76. Find the modal class & median class. U

77. Write the following distribution as less than type cumulative frequency distribution : S

78. Find the mode .U

79. Find median & modal class .U

80. Find the median & modal class of the following distribution. U

81. Write the following distribution as less than type frequency distribution. S

82. Find the mean of the following distributions. U

83. Write the following distribution as less than type cumulative frequency distribution. S

84. Find the modal class & median class for the following distribution. U

85. Find the mean from the following .U

86. Find the upper limit of the modal class of the above frequency distribution. U

87. Find the mode from the following frequency distribution. U

88. Find the median of the following data. U

89. Find the mode of the following data .U

90. Write a frequency distribution table for the following data. S

91. Write the frequency distribution table for the following. S

92. Find the mode of the following data .U

93. Find the range and the coefficient of range of 43, 24, 38, 56, 22, 39, 45. K

94. The largest of 50 measurements is 3.84 kg If the range is 0.46 kg, find the smallest

measurement. K

95. Find the median, when the mode is 120.8 and the mean is 128. U

96. Find the mode of the scores,

5, 5, 7, 6, 6, 3, 2, 6, 7, 5, 3, 7, 4, 5, 4 .U

97. The table below shows the number of workers doing various jobs in a factory and their

daily wages.

What is the mean daily wage? A

98. Find the mode of the given data .U

99. Calculate the median of the following data .U

100. Find the mean .U

Short answer type questions(3 marks)

102. Find the mean of the following frequency distribution .U

103. Find the mode from the following data . U

104. The mean of following distribution is 25. Find P. U

105. Find the mode of the following .U

106. Find the mode from the following distribution .U

107. Find the mean of the given frequency table .U

108. Find the median .U

109. Draw more than type table for the following & obtain the median. S

110. Find the mode of the following frequency distribution. U

111. Write the distribution as more than type cumulative frequency distribution. S

112. Find the median .U

113. Draw a more than type ogive table for the following distribution and hence obtain the

median. S

114. The median class of a frequency distribution is 120−140. The frequency & cumulative

frequency of the class preceding to the median class are 16 & 24 respectively. Find the

sum of the frequencies if the median is 135 .U

115. Find the mean of the following frequency distribution. U

116. Find the median of the following data .U

117. Find the mode of the following data .U

118. Find the median of the following data. .U

119. Calculate the mode of the following frequency distribution. U

120. Compute the median for the following data .S

121. Calculate the mode of the following frequency distribution .U

122. Find the median of the following data. U

123. Find the mode of the following data .U

124. Find the median of the following data. U

125. Find the median daily expenses from the following data. U

126. Find the A.M. for the following distribution table using Deviation method. U

127. The table below shows the classification of the numbers of a committee according to their

age.

Calculate the median age of the members. A

128. The table shows the classification of 100 families in a locality according to the amount

paid against their electricity bill.

Find the median of the amount paid. A

129. The table below classifies 60 students in a class according to their heights.

Find the median of the amount paid. A

130. Find the mean by deviation method .U

Long answer type questions (4 marks)

131. Find the median from the following cumulative frequency distribution. S

132. Find the median from the following table .U

133. Find the mean of the following data .U

134. The mean of the following frequency distribution is 34.9. Find the value of P .U

135. Find the missing frequency if the mean is 17.52 .U

136. Find a more than type ogive for the following frequency distribution and hence find the

median. S

137. Draw a more than ogive table for the following frequency distribution & hence find the

median. S

138. Find mean from the following table. U

139. Find the mode of the following frequency distribution. U

140. Convert the following frequency distribution into more than type & less than type and

hence find the median. S

141. From the following frequency distribution find the values of a, b, c, d, e if the total no. of

students in a class is 60. S

142. Convert the following data into more than type ogive & find median. S

143. Find the mean marks from the following data .S

144. Find the median from the following distribution .S

145. Find the mean of the following data using step deviation method. U

146. Write the frequency distribution table for the following data. S

147. The table below shows the number students in the Maths Club of a school, classified

according to their heights.

Calculate the mean height. A

148. Find the mean of the following grouped data by shortcut method : U

149. Find the median of the following frequency distribution table: U