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Statistics Class 10 Maths CBSE Important Questions With Solutions

Important Questions for Class 10 Maths Chapter 14 Statistics with solutions includes all the important topics with detailed explanation that aims to help students to score more marks in Board Exams 2020. Students who are preparing for their Class 10 exams must go through Important Questions for Class 10 Math Chapter 14 Statistics.

Important Questions for Class 10 Maths Chapter 14 Statistics

Expert teachers at CBSETuts.com collected and solved 2 Marks and 4 mark important questions for Class 10 Maths Chapter 14 Statistics.

MathsScienceEnglishSocialHindi AHindi B

2016
Very Short Answer Type Questions [1 Mark]

Question 1.
Find mode, using an empirical relation, when it is given that mean and median are 10.5 and 9.6 respectively.
Solution:
Mean = 10.5 and median = 9.6
Empirical relation: 3 Median = Mode + 2 Mean
3(9.6) = Mode + 2(10.5)
28.8 = Mode + 21
Mode = 28.8 – 21 = 7.8

Use Median Calculator. Enter the list of real numbers. separated by commas, check the data entered and then press “Calculate Median”.

Question 2.
In a frequency distribution, if a = assumed mean = 55,∑ fi = 100, h = 10 and ∑ƒiμi = -30, then find the mean of the distribution
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 1

Short Answer Type Questions I [2 Marks]

Question 3.
Statistics Class 10 Maths CBSE Important Questions With Solutions 2
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 3

Question 4.
Statistics Class 10 Maths CBSE Important Questions With Solutions 4
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 5

Short Answer Type Questions II [3 Marks]

Question 5.
The following data gives the information on the observed life times (in hours) of 150 electrical components
Statistics Class 10 Maths CBSE Important Questions With Solutions 6
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 7

Question 6.
The average score of boys in the examination of a school is 71 and that of the the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination.
Solution:
Let number of boys in the school be x
Average score of boys = 71
Total score of boys in the examination of the school = 71xx = 71x
Let number of girls in the school be y
Average score of girls = 73
Total score of girls in the examination of the school = 73 x y = 73y
Now,
average score of the school in examination = 71.8
Statistics Class 10 Maths CBSE Important Questions With Solutions 8

An online age calculator helps to calculate the exact age in terms of years, months, days, and tells the remaining months & days on your next birthday.

Question 7.
Statistics Class 10 Maths CBSE Important Questions With Solutions 9
Statistics Class 10 Maths CBSE Important Questions With Solutions 10
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 11
Statistics Class 10 Maths CBSE Important Questions With Solutions 12

Long Answer Type Questions [4 Marks]

Question 8.
Statistics Class 10 Maths CBSE Important Questions With Solutions 13
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 14
Statistics Class 10 Maths CBSE Important Questions With Solutions 15
Statistics Class 10 Maths CBSE Important Questions With Solutions 16
Statistics Class 10 Maths CBSE Important Questions With Solutions 17

Question 9.
Statistics Class 10 Maths CBSE Important Questions With Solutions 18
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 19

Question 10.
Statistics Class 10 Maths CBSE Important Questions With Solutions 20
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 21

2015

Very Short Answer Type Question [1 Mark]

Question 11.
Given below is a cumulative frequency distribution of “less than type”.
Statistics Class 10 Maths CBSE Important Questions With Solutions 22
Change the above data into a continuous grouped frequency distribution
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 23

Short Answer Type Question I [2 Mark]

Question 12.
The following table shows the distribution of weights of 100 candidates appearing for a competition. Determine the modal weight.
Statistics Class 10 Maths CBSE Important Questions With Solutions 24
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 25

Short Answer Type Question II[3 Marks]

Question 13.
If the mean of the following distribution is 54, find the missing frequency x:
Statistics Class 10 Maths CBSE Important Questions With Solutions 26
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 27

Question 14.
Draw a ‘less than type’ ogive for the following frequency distribution.
Statistics Class 10 Maths CBSE Important Questions With Solutions 28
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 29
Statistics Class 10 Maths CBSE Important Questions With Solutions 30

Long Answer Type Question [4 Mark]

Question 15.
The lengths of 50 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table
Statistics Class 10 Maths CBSE Important Questions With Solutions 31
Find the mean length of the leaves.
Solution:
Given frequency distribution is not continuous. So first we have to make it continuous.
Statistics Class 10 Maths CBSE Important Questions With Solutions 32

Question 16.
In a hospital, during the month of October 2013, number of patients admitted for dengue and their ages are as follows
Statistics Class 10 Maths CBSE Important Questions With Solutions 33
Find the mean and median age of patients.
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 34

2014

Short Answer Type Question I [2 Mark]

Question 17.
Ramesh is a cricket player. He played 50 matches in a year. His data regarding runs scored is given below. Calculate his average score.
Statistics Class 10 Maths CBSE Important Questions With Solutions 35
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 36

Question 18.
The width of 50 leaves of a plant were measured in mm and their cumulative frequency distribution is shown in the following table. Make frequency distribution table for this
Statistics Class 10 Maths CBSE Important Questions With Solutions 37
Solution:
Frequency distribution table is as follows:
Statistics Class 10 Maths CBSE Important Questions With Solutions 38

Question 19.
Find the mode of the following frequency distribution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 39
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 40

Short Answer Type Questions II [3 Marks]

Question 20.
For helping poor girls of their class, students saved pocket money as shown in the following table:
Statistics Class 10 Maths CBSE Important Questions With Solutions 41
Find mean and median or this data.
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 42
Question 21.
For the following distribution, draw a ‘less than type’ ogive and from the curve, find median.
Statistics Class 10 Maths CBSE Important Questions With Solutions 43
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 44
Statistics Class 10 Maths CBSE Important Questions With Solutions 45
From graph, median = 54.

Question 22.
The Median of the following distribution is 35.Find the value of x:
Statistics Class 10 Maths CBSE Important Questions With Solutions 46
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 47

Question 23.
Find the median of the following data
Statistics Class 10 Maths CBSE Important Questions With Solutions 48
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 49

Question 24.
In a school, weights of 62 teachers was recorded as follows:
Statistics Class 10 Maths CBSE Important Questions With Solutions 50
Draw a ‘more than type’ ogive for this distribution and hence obtain median from the curve.
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 51
Statistics Class 10 Maths CBSE Important Questions With Solutions 52

From graph median = 64.

Long Answer Type Questions [4 Marks]

Question 25.
Find the missing frequencies (f1, f2 and /3) in the following frequency distribution when it is given that f2 :f3 = 4: 3 and mean = 50.
Statistics Class 10 Maths CBSE Important Questions With Solutions 53
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 54

Question 26.
Draw a less than type give for the following distribution
Statistics Class 10 Maths CBSE Important Questions With Solutions 55
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 56
Statistics Class 10 Maths CBSE Important Questions With Solutions 57

Question 27.
Literacy rates of 40 cities is given in the following table. If it is given that mean literacy rate is 63.5, then find the missing frequencies x and y.
Statistics Class 10 Maths CBSE Important Questions With Solutions 58
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 59

Question 28.
If median height of 50 students of a class in the following frequency distribution is 144 cm, find the missing frequencies x and y
Statistics Class 10 Maths CBSE Important Questions With Solutions 60
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 61
Statistics Class 10 Maths CBSE Important Questions With Solutions 62

2013

Short Answer Type Questions I [2 Marks]

Question 29.
The following distribution given below gives the daily income of 50 workers in a factory
Statistics Class 10 Maths CBSE Important Questions With Solutions 63
Convert the above distribution to a less than type cumulative frequency distribution
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 64

Question 30.
Make a frequency distribution table for the given table:
Statistics Class 10 Maths CBSE Important Questions With Solutions 65
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 66

Short Answer Type Questions II [3 Marks]

Question 31.
The mean of the following frequency distribution is 62.8. Find the missing frequency x
Statistics Class 10 Maths CBSE Important Questions With Solutions 67
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 68

Question 32.
The weights of tea in 70 packets are shown in the following table.
Statistics Class 10 Maths CBSE Important Questions With Solutions 69
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 70

Question 33.
Find the mode of the following data
Statistics Class 10 Maths CBSE Important Questions With Solutions 71
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 72

Question 34.
If the mode of the following distribution is 57.5, find the value of x
Statistics Class 10 Maths CBSE Important Questions With Solutions 73
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 74

Long Answer Type Questions [4 Marks]

Question 35.
Find the mean, median and mode of the following data:
Statistics Class 10 Maths CBSE Important Questions With Solutions 75
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 76
Statistics Class 10 Maths CBSE Important Questions With Solutions 131

2012

Short Answer Type Question I [2 Marks]

Question 36.
Convert the following frequency distribution to a more than type cumulative frequency distribution
Statistics Class 10 Maths CBSE Important Questions With Solutions 77
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 78

Short Answer Type Question II [3 Marks]

Question 37.
Weekly income of 600 families is given below
Statistics Class 10 Maths CBSE Important Questions With Solutions 79
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 80

Long Answer Type Questions [4 Marks]

Question 38.
Find the value of fx from the following data, if its mode is 65.
Statistics Class 10 Maths CBSE Important Questions With Solutions 81
where frequency 6,8,f1, and 12 are in ascending order
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 82
mode=65
modal class=60-80 as its frequency is 12
l=60,f=12,f0=f1,f2=6,h=20
Statistics Class 10 Maths CBSE Important Questions With Solutions 85

2011

Short Answer Type Questions I [2 Marks]

Question 39.
Convert the following data to a less than type distribution.
Statistics Class 10 Maths CBSE Important Questions With Solutions 84
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 86

Question 40.
Write the frequency distribution table for the following data:
Statistics Class 10 Maths CBSE Important Questions With Solutions 87
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 88
Question 41.
Calculate mode of the following data
Statistics Class 10 Maths CBSE Important Questions With Solutions 89
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 90

Short Answer Type Questions II [3 Marks]

Question 42.
Find ‘p’ if the mean of the given data is 15.45.
Statistics Class 10 Maths CBSE Important Questions With Solutions 91
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 92
Statistics Class 10 Maths CBSE Important Questions With Solutions 93

Question 43.
The median of the distribution given below is 14.4.Find the values of the x,y.if the sum of frequency is 20.
Statistics Class 10 Maths CBSE Important Questions With Solutions 94
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 95
Statistics Class 10 Maths CBSE Important Questions With Solutions 96

Long Answer Type Questions [4 Marks]

Question 44.
Draw a less than type ogive of the following distribution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 97
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 98
Statistics Class 10 Maths CBSE Important Questions With Solutions 99
median=42

Question 45.
Find the median by drawing both types of gives.
Statistics Class 10 Maths CBSE Important Questions With Solutions 100
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 101
Statistics Class 10 Maths CBSE Important Questions With Solutions 102
Statistics Class 10 Maths CBSE Important Questions With Solutions 103
curves intersect at(80.4,17.5)
median=80.4.

2010

Long Answer Type Questions [4 Marks]

Question 46.
Find the mean, mode and median of the following frequency distribution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 104
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 105

Question 47.
Draw ‘less than ogive’ and ‘more than ogive’ for the following distribution and hence find its median
Statistics Class 10 Maths CBSE Important Questions With Solutions 106
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 107
Statistics Class 10 Maths CBSE Important Questions With Solutions 108
we notice both curves intersect at (60,50)
median =60

Question 48.
Draw ‘less than ogive’ and ‘more than ogive’ for the following distribution and hence find its median.
Statistics Class 10 Maths CBSE Important Questions With Solutions 109
Solution:
table for “less than ogive’ and ‘more than ogive”
Statistics Class 10 Maths CBSE Important Questions With Solutions 110
Statistics Class 10 Maths CBSE Important Questions With Solutions 111
we notice curves intersect at(50,50)
median=50.

Question 49.
Draw ‘less than ogive’ and ‘more than ogive’ for the following distribution and hence find its median
Statistics Class 10 Maths CBSE Important Questions With Solutions 112
Solution:
table for less than ogive’ and ‘more than ogive’
Statistics Class 10 Maths CBSE Important Questions With Solutions 113
Statistics Class 10 Maths CBSE Important Questions With Solutions 114
we notice curves intersect at(58.3,50)
median=58.30

Question 50.
If the mean of the following frequency distribution is 65.6, find the missing
Statistics Class 10 Maths CBSE Important Questions With Solutions 115
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 116

Question 51.
If the mean of the following frequency distribution is 91, find the missing frequencies (f1,f2):
Statistics Class 10 Maths CBSE Important Questions With Solutions 117
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 118

Question 52.
If the mean of the following frequency distribution is 145, find the missing frequencies (f1,f2):
Statistics Class 10 Maths CBSE Important Questions With Solutions 119
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 120

2009

Very Short Answer Type Questions [1 Mark]

Question 53.
Write the median class of the following distribution :
Statistics Class 10 Maths CBSE Important Questions With Solutions 121
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 122
N=50
N/2=25
Median Class=30-40

Question 54.
What is the lower limit of the modal class of the following distribution
Statistics Class 10 Maths CBSE Important Questions With Solutions 123
Solution:
Modal class =40-50
lower limit=40

Long Answer Type Questions [4 Marks]

Question 55.
The following table gives the daily income of 50 workers of a factory:
Statistics Class 10 Maths CBSE Important Questions With Solutions 124
Find the mean, mode and median of the above data.
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 125

Question 56.
During the medical check-up of 35 students of a class their weights were recorded as follows:
Statistics Class 10 Maths CBSE Important Questions With Solutions 126
Draw a less than type and a more than type ogive from the given data. Hence obtain the median weight from the graph
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 127
Statistics Class 10 Maths CBSE Important Questions With Solutions 128
we notice both the curves intersect at(17.5,46.5)
Median weight=46.5kg

Question 57.
Find the mode,median and mean of the following data
Statistics Class 10 Maths CBSE Important Questions With Solutions 129
Solution:
Statistics Class 10 Maths CBSE Important Questions With Solutions 130

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