Important Questions for Class 10 Maths Chapter 14 Statistics

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Important Questions for Class 10 Maths Chapter 14 Statistics

Statistics Class 10 Important Questions Very Short Answer (1 Mark)

Question 1.
In a continuous frequency distribution, the median of the data is 21. If each observation is increased by 5, then find the new median. (2015)
Solution:
New median = 21 + 5 = 26

Question 2.
From the following frequency distribution, find the median class: (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 1
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 2
∴ Median class 1700 – 1850.

Question 3.
Consider the following distribution, find the frequency of class 30-40. (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 3
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 4
∴ Frequency of class 30 – 40 = 3

Question 4.
Following table shows sale of shoes in a store during one month: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 5
Find the model size of the shoes sold.
Solution:
Maximum no. of pairs sold = 25 (size 5)
∴ Modal size of shoes = 5

Question 5.
Weekly household expenditure of families living in a housing society are shown below: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 6
Find the upper limit of the modal class.
Solution:
Maximum frequency = 48
∴ Modal class = 9,000 – 12,000
Upper limit of the modal class = 12,000

Statistics Class 10 Important Questions Short Answer-I (2 Marks)

Question 6.
The mean of the following data is 18.75. Find the value of P: (2012, 2017D)
Important Questions for Class 10 Maths Chapter 14 Statistics 7
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 8

Question 7.
Data regarding heights of students of Class X of Model School, Dehradun is given below. Calculate the average height of students of the class. (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 9
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 10

Question 8.
From the following cumulative frequency table, construct a frequency distribution table: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 11
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 12

Question 9.
Convert the following frequency distribution to a ‘more than’ type cumulative frequency distribution. (2012)
Important Questions for Class 10 Maths Chapter 14 Statistics 13
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 14

Question 10.
The distribution given below gives the daily income of 50 workers in a factory: (2017D)
Important Questions for Class 10 Maths Chapter 14 Statistics 15
Convert the above distribution to a less than type cumulative frequency distribution.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 16

Question 11.
Find the mode of the following frequency distribution: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 17
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 18
Important Questions for Class 10 Maths Chapter 14 Statistics 19

Question 12.
Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students. (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 20
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 21
∴ Required pocket money = ₹86.32 (approx.)

Question 13.
Find the median of the data using an empirical formula, when it is given that mode = 35.3 and mean = 30.5. (2014)
Solution:
Mode = 3(Median) – 2(Mean)
35.3 = 3(Median) – 2(30.5)
35.3 = 3(Median) – 61
96.3 = 3 Median
Median = (frac{96.3}{3}) = 32.1

Question 14.
Show that the mode of the series obtained by combining the two series S1 and S2 given below is different from that of S1 and S2 taken separately: (2015)
S1 : 3, 5, 8, 8, 9, 12, 13, 9, 9
S2 : 7, 4, 7, 8, 7, 8, 13
Solution:
In S1 : Number 9 occurs 3 times (maximum)
∴ Mode of S1 Series = 9
In S2 : Number 7 occurs 3 times (maximum)
∴ Mode of S, Series = 7
After combination:
In S1 & S2 : No. 8 occurs 4 times (maximum)
∴ Mode of S1 & S2 taken combined = 8
So, mode of S1 & S2 combined is different from that of S1 & S2 taken separately.

Statistics Class 10 Important Questions Short Answer-II (3 Marks)

Question 15.
Find the mean of the following data. (2012)
Important Questions for Class 10 Maths Chapter 14 Statistics 22
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 23

Question 16.
The following table gives the literacy rate (in %) in 40 cities. Find the mean literacy rate: (2012)
Important Questions for Class 10 Maths Chapter 14 Statistics 24
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 25

Question 17.
If the mean of the following distribution is 50, find the value of p: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 26
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 27

Question 18.
The mean of the following frequency distribution is 62.8. Find the missing frequency x. (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 28
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 29

Question 19.
The frequency distribution table of agricultural holdings in a village is given below: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 30
Find the Mean area held by a family.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 31

Question 20.
Monthly pocket money of students of a class is given in the following frequency distribution:
Important Questions for Class 10 Maths Chapter 14 Statistics 32
Find mean pocket money using step deviation method. (2014)
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 33

Question 21.
Find the mean of the following distribution by Assumed Mean Method: (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 34
Important Questions for Class 10 Maths Chapter 14 Statistics 35
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 36

Question 22.
Find the mean and median for the following data: (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 37
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 38

Question 23.
For helping poor girls of their class, students saved pocket money as shown in the following table: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 39
Find mean and median for this data.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 40

Question 24.
Weekly income of 600 families is given below:
Important Questions for Class 10 Maths Chapter 14 Statistics 41
Find the median. (2012)
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 42
Important Questions for Class 10 Maths Chapter 14 Statistics 43

Question 25.
Find the median for the following distribution: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 44
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 45

Question 26.
Heights of students of class X are given in the following frequency distribution: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 46
Find the modal height.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 47
Maximum frequency is 20
∴ Modal class is 160 – 165
Important Questions for Class 10 Maths Chapter 14 Statistics 48
∴ The modal height = 163 cm

Question 27.
A medical camp was held in a school to impart health education and the importance of excercise to children. During this camp, a medical check of 35 students was done and their weights were recorded as follows: (2016)
Important Questions for Class 10 Maths Chapter 14 Statistics 49
Compute the modal weight.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 50
∴ Modal weight = 46.9 kg

Question 28.
The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of number of boys to the number of girls who appeared in the examination. (2015)
Solution:
Let the number of boys = n1
and number of girls = n2
Important Questions for Class 10 Maths Chapter 14 Statistics 51
Important Questions for Class 10 Maths Chapter 14 Statistics 52
∴ No. of boys : No. of girls = 3 : 2

Question 29.
Following is the age distribution of dengue patients admitted in a hospital during a week of October, 2013: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 53
Draw a ‘less than type’ ogive for the above distribution. Also, obtain median from the curve.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 54

Question 30.
The lengths of leaves of a plant are measured correct to the nearest mm and the data obtained is represented as the following frequency distribution: (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 55
Important Questions for Class 10 Maths Chapter 14 Statistics 56
Draw a ‘more than type’ ogive for the above data.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 57

Statistics Class 10 Important Questions Long Answer (4 Marks)

Question 31.
The mean of the following frequency distribu tion is 53. But the frequencies f1 and f2 in the classes 20-40 and 60-80 are missing. Find the missing frequencies: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 58
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 59
⇒ 2730 + 30f1 + 70f2 = 5300
⇒ 30f1 + 70f2 = 5300 – 2730 = 2570
⇒ 3f1 + 7f2 = 257 …[Dividing by 10
⇒ 3f1 +7(47 – f1) = 257 . [From (i)
⇒ 3f1 + 329 – 7f1 = 257
⇒ -4f1 = 257 – 329 = -72
⇒ f1 = (frac{-72}{-4}) = 18
Putting the value of f1 in (i), we get
f2 = 47 – f1
⇒ f2 = 47 – 18 = 29
∴ f1 = 18, f2 = 29

Question 32.
The mean of the following frequency distribution is 62.8 and the sum of frequencies is 50. Find the missing frequencies f1 and f2: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 60
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 61
⇒ 2060 + 30f1 + 70f2 = 3140
⇒ 30f1 + 70f2 = 3140 – 2060 = 1080
⇒ 3f1 + 7f2 = 108 …[Dividing by 10
⇒ 3f1 + 7(20 – f1) = 108 … [From (i)
⇒ 3f1 + 140 – 7f1 = 108
⇒ -4f1 = 108 – 140 = -32 .
∴ f1 = 8
Putting the value of f1 into (i), we get
f2 = 20 – 8 = 12
∴ f2 = 12

Question 33.
In the table below, heart-beats of 30 women are recorded. If mean of the data is 76, find the missing frequencies x and y. (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 62
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 63
⇒ 1978 + 66.5x + 84.5y = 2280
⇒ 1978 + 66.5x + 84.5(4 – x) = 2280 … [From (i)
⇒ 1978 + 66.5x + 338 – 84.5x = 2280
⇒ 1978 + 338 – 2280 = 84.5x – 66.5x
⇒ 36 = 18x ⇒ x = 2
From (i), y = 4 – x = 4 – 2 = 2 ∴ x = 2, y = 2

Question 34.
The following table gives the daily income of 50 workers of a factory. Draw both types (“less than type” and “greater than type”) ogives. (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 64
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 65
Important Questions for Class 10 Maths Chapter 14 Statistics 66

Question 35.
Find the values of x and y if the median for the following data is 31. (2012)
Important Questions for Class 10 Maths Chapter 14 Statistics 67
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 68
⇒ 18 – x = (9 – x)10
⇒ 18 – x = 90 – 10x
⇒ -x + 10x = 90 – 18
⇒ 9x = 72
⇒ x = 8
Putting the value of x in (i), we have
y = 18 – 8 = 10
∴ x = 8, y = 10

Question 36.
The median of the following data is 525. Find x and y if the sum of all frequencies is 100: (2012, 2017 D)
Important Questions for Class 10 Maths Chapter 14 Statistics 69
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 70

Question 37.
Find the missing frequencies f1 and f2 in the following frequency distribution table, if N = 100 and median is 32. (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 71
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 72
Important Questions for Class 10 Maths Chapter 14 Statistics 73

Question 38.
Find the median of the following data: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 74
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 75

Question 39.
The frequency distribution of weekly pocket money received by a group of students is given below: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 76
Draw a ‘more than type’ ogive and from it, find median. Verify median by actual calculations.
Solution:
n = 90 …[Given
Important Questions for Class 10 Maths Chapter 14 Statistics 77
Important Questions for Class 10 Maths Chapter 14 Statistics 78

Question 40.
Draw “less than ogive” and “more than ogive” for the following distribution and hence find its median. (2012)
Important Questions for Class 10 Maths Chapter 14 Statistics 79
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 80
Important Questions for Class 10 Maths Chapter 14 Statistics 81

Question 41.
Draw: (a) more than ogive and (2017OD)
(b) less than ogive for the following data
Also find its median.
Important Questions for Class 10 Maths Chapter 14 Statistics 82
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 83
Important Questions for Class 10 Maths Chapter 14 Statistics 84

Question 42.
Draw a more than ogive for the data given below which gives the marks of 100 students: (2012, 2017D)
Important Questions for Class 10 Maths Chapter 14 Statistics 85
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 86

Question 43.
For the following distribution, draw a ‘more than Ogive’ and hence find the median: (2013)
Important Questions for Class 10 Maths Chapter 14 Statistics 87
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 88

Question 44.
School held sports day in which 150 students participated. Ages of students are given in the following frequency distribution: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 89
For the above data, draw a ‘more than type’ ogive and from the curve, find median. Verify it by actual calculations.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 90
Important Questions for Class 10 Maths Chapter 14 Statistics 91

Question 45.
In a class test, marks obtained by 120 students are given in the following frequency distribution. If it is given that mean is 59, find the missing frequencies x and y. (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 92
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 93
Important Questions for Class 10 Maths Chapter 14 Statistics 94

Question 46.
Mode of the following frequency distribution is 65 and sum of all the frequencies is 70. Find the missing frequencies x and y. (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 95
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 96
54 + x + y = 70 … [Given
x + y = 70 – 54 = 16 …(i)
∴ Mode = 65
Modal Class is 60 – 80
Important Questions for Class 10 Maths Chapter 14 Statistics 97

Question 47.
Find the mode of the following frequency distribution: (2015)
Important Questions for Class 10 Maths Chapter 14 Statistics 98
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 99

Question 48.
Cost of Living Index for some period is given in the following frequency distribution: (2014)
Important Questions for Class 10 Maths Chapter 14 Statistics 100
Find the mode and median for above data.
Solution:
Important Questions for Class 10 Maths Chapter 14 Statistics 101
Important Questions for Class 10 Maths Chapter 14 Statistics 102

Important Questions for Class 10 Maths

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