NCERT Solutions For Class 10 Maths Chapter 14 Statistics

NCERT Solutions For Class 10 Maths Chapter 14 Statistics

NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1

Ex 14.1 Class 10 Maths Question 1.
A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q1
Which method did you use for finding the mean, and why?
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.1 PDF Download Q1

You can also download the free PDF of  Ex 14.1 Class 10 Statistics NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

 

Ex 14.1 Class 10 Maths Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q2
Find the mean daily wages of the workers of the factory by using an appropriate method.
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.1 PDF Download Q2

Ex 14.1 Class 10 Maths Question 3.
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ₹ 18. Find the missing frequency f.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q3
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.1 PDF Download Q3

Ex 14.1 Class 10 Maths Question 4.
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q4
Solution:
Ex 14.1 Class 10 Maths NCERT Solutions PDF Download Q4

Ex 14.1 Class 10 Maths Question 5.
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q5
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Solution:
Ex 14.1 Class 10 Maths NCERT Solutions PDF Download Q5

Ex 14.1 Class 10 Maths Question 6.
The table below shows the daily expenditure on food of 25 households in a locality.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q6
Find the mean daily expenditure on food by a suitable method.
Solution:
Exercise 14.1 Class 10 Maths NCERT Solutions PDF Download Q6

Ex 14.1 Class 10 Maths Question 7.
To find out the concentration of SO2 in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q7
Find the mean concentration of SO2 in the air.
Solution:
Exercise 14.1 Class 10 Maths NCERT Solutions PDF Download Q7

Ex 14.1 Class 10 Maths Question 8.
A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q8
Solution:
Chapter 14 Maths Class 10 NCERT Solutions Ex 14.1 PDF Download Q8

Ex 14.1 Class 10 Maths Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Q9
Solution:
Chapter 14 Maths Class 10 NCERT Solutions Ex 14.1 PDF Download Q9

Class 10 Maths Statistics Mind Maps

Basic Terms

Class limits : Suppose mark obtained by all of the students are divided into class intervals 25 – 35, 35 – 45 and so interval on.
In class interval 25 – 35, 25 is called lower class limit and 35 is called upper class limit.
Class size : The difference between upper and lower class limit.
Class mark : It is given by
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 1

Ungrouped and Grouped Data

The data obtained in original form are called raw data or ungrouped data.
To put the data in a more condensed form, we make groups of suitable size, and mention the frequency of each group. Such a table is called grouped data.

Mean

For Ungrouped:
Consider ‘n’ observations in ungrouped data as : x1, x2, x3, …. xn. The mean of these observations is:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 2
(i) Direct method:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 3
where ‘fi‘ is the frequency corresponding to the class mark ‘xi
(ii) Assumed mean method:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 4
Where A is assumed mean and di = xi – A
(iii) step deviation method:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 5

Mode

(i) For Ungrouped Data:
The mode is that observation which occurs most frequently, i.e., an observation with maximum frequency.
(ii) For Grouped Data:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 6
l =lower limit of the modal class,
f1 = frequency of the modal class
2 = frequency of the class suceeding the modal class,
h = size of the class interval,
f0 = frequency of the class preceeding the modal class.
The class with the maximum frequency is called modal class.

Median

Median is a measure of central tendency which gives the value of the middle-most observation in the data.
(i) For Ungrouped Data:
Arrange the data in ascending order.
If number of data n is odd, then the median is (n+1/2)th observation.
If number of data n is even, then the median is the average of (n/2)th and (n/2+1)th observations.

(ii) For Grouped Data:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.1 Mind Map 7
l = lower limit of the median class,
c.f = cumulative frequency of the class proceeding the median class,
f = frequency of the median class,
h = class size,
n = number of observations.
The class whose cumulative frequency is greater than (and nearest to) n/2 is called median class.

Relationship Between Mean, Mode and Median
3 Median = Mode + 2 Mean

Cumulative Frequency Curve (Ogive)

(i) The smooth free hand curve is formed by joining the points (xi, fi) where x; is the upper limit of a class and f is the corresponding c.f. The curve so obtained is called a cumulative frequency curve, or an ogive of the less than type.
(ii) The smooth free hand curve is formed by joining the points (xi, fi) where Xi is the lower limit of a class and f is the corresponding c.f. The curve so obtained is called a cumulative frequency curve, or an ogive of the more than type.

Median by Graph

(i) Draw the ogive of the less than type and ogive of the more than type on the same axis. The two ogives will intersect each other at a point. From this point, if we draw a perpendicular on the x-axis, the point at which it cuts the x-axis gives us the median.
(ii) Draw the ogive of the less than type, then locate n/2 on the y-axis (n = number of observations).

From this point on y-axis, draw a line parallel to x-axis cutting the less than ogive at a point. From this point draw a perpendicular on the x-axis, the point at which the perpendicular cuts the x-axis gives us the median.

NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2

Ex 14.2 Class 10 Maths Question 1.
The following table shows the ages of the patients admitted in a hospital during a year.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q1
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.2 PDF Download Q1

Ex 14.2 Class 10 Maths Question 2.
The following data gives information on the observed lifetimes (in hours) of 225 electrical components:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q2
Determine the modal lifetimes of the components.
Solution:
Ex 14.2 Class 10 Maths NCERT Solutions PDF Download Q2

Ex 14.2 Class 10 Maths Question 3.
The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q3
Solution:
Exercise 14.2 Class 10 Maths NCERT Solutions Q3

Ex 14.2 Class 10 Maths Question 4.
The following distribution gives the state-wise teacher- student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q4
Solution:
Chapter 14 Maths Class 10 NCERT Solutions Ex 14.2 PDF Download Q4
Chapter 14 Maths Class 10 NCERT Solutions Ex 14.2 PDF Download Q4.1

Ex 14.2 Class 10 Maths Question 5.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q5
Find the mode of the data.
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.2 PDF Download Q5

Ex 14.2 Class 10 Maths Question 6.
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.2 Q6
Solution:
Exercise 14.2 Class 10 Maths NCERT Solutions PDF Download Q6

NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3

Ex 14.3 Class 10 Maths Question 1.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q1
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q1
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q1.1

Ex 14.3 Class 10 Maths Question 2.
If the median of the distribution given below is 28.5, find the values of x and y.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q2
Solution:
Ex 14.3 Class 10 Maths NCERT Solutions pdf download Q2
Ex 14.3 Class 10 Maths NCERT Solutions pdf download Q2.1

Ex 14.3 Class 10 Maths Question 3.
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q3
Solution:
Exercise 14.3 Class 10 Maths NCERT Solutions pdf download Q3

Ex 14.3 Class 10 Maths Question 4.
The lengths of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q4
Find the median length of the leaves.
Solution:
Exercise 14.3 Class 10 Maths NCERT Solutions pdf download Q4
Exercise 14.3 Class 10 Maths NCERT Solutions pdf download Q4.1

Ex 14.3 Class 10 Maths Question 5.
The following table gives the distribution of the lifetime of 400 neon lamps:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q5
Find the median lifetime of a lamp.
Solution:
Chapter 14 Maths Class 10 NCERT Solutions Ex 14.3 pdf download Q5

Ex 14.3 Class 10 Maths Question 6.
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q6
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q6
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q6.1
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q6.2

Ex 14.3 Class 10 Maths Question 7.
The distribution below gives the weight of 30 students of a class. Find the median weight of the students.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3 Q7
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.3 pdf download Q7

NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.4

Ex 14.4 Class 10 Maths Question 1.
The following distribution gives the daily income of 50 workers of a factory.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.4 Q1
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Solution:
Statistics Class 10 Maths NCERT Solutions Ex 14.4 pdf download Q1
Statistics Class 10 Maths NCERT Solutions Ex 14.4 pdf download Q1.1

Ex 14.4 Class 10 Maths Question 2.
During the medical check-up of 35 students of a class, their weights were recorded as follows:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.4 Q2
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Solution:
Ex 14.4 Class 10 Maths NCERT Solutions pdf download
Ex 14.4 Class 10 Maths NCERT Solutions pdf download Q2.1

Ex 14.4 Class 10 Maths Question 3.
The following table gives production yield per hectare of wheat of 100 farms of a village.
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.4 Q3
Change the distribution to a more than type distribution, and draw its ogive.
Solution:
Exercise 14.4 Class 10 Maths NCERT Solutions pdf download Q3
Exercise 14.4 Class 10 Maths NCERT Solutions pdf download Q3.1

Statistics Class 10 Extra Questions Maths Chapter 14

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Statistics-CBSE-Class-10-Maths-Extra-Questions-1-dStatistics-CBSE-Class-10-Maths-Extra-Questions-2-a
Statistics-CBSE-Class-10-Maths-Extra-Questions-2-b
Statistics-CBSE-Class-10-Maths-Extra-Questions-3-a
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Statistics-CBSE-Class-10-Maths-Extra-Questions-6-a
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Statistics-CBSE-Class-10-Maths-Extra-Questions-7
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Statistics-CBSE-Class-10-Maths-Extra-Questions-9-a
Statistics-CBSE-Class-10-Maths-Extra-Questions-9-b

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 = 96.3/3 = 32.1

Question 14.
Show that the mode of the series obtained by combining the two series S1 and Sgiven below is different from that of Sand 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 = 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

CBSE Class 10 Maths Notes Chapter 14 Statistics

MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x1, x2, x3 … xn, is
Statistics Class 10 Notes Maths Chapter 14 1

MEAN [Grouped Data]: The mean for grouped data can be found by the following three methods:
(i) Direct Mean Method:
Statistics Class 10 Notes Maths Chapter 14 2
Class Mark = Upper Class Limit + Lower Class Limit / 2

Note: Frequency of a class is centred at its mid-point called class mark.

(ii) Assumed Mean Method: In this, an arbitrary mean ‘a’ is chosen which is called, ‘assumed mean’, somewhere in the middle of all the values of x.
Statistics Class 10 Notes Maths Chapter 14 3
…[where di = (xi – a)]

(iii) Step Deviation Method:
Statistics Class 10 Notes Maths Chapter 14 4
….. [where ui=di/h , where h is a common divisor of di]

MEDIAN: Median is a measure of central tendency which gives the value of the middle-most observation in the data.
Statistics Class 10 Notes Maths Chapter 14 5
…where[l = Lower limit of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of preceding class; h = Class size]

(iii) Representing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type. The median of grouped data can be obtained graphically as the x-coordinate of the point of intersection of the two ogives for this data.

Mode:
(i) Ungrouped Data: The value of the observation having maximum frequency is the mode.
(ii) Grouped Data:
Statistics Class 10 Notes Maths Chapter 14 6
…where[l = Lower limit of modal class; f1 = Frequency of modal class; f0 = Frequency of the class preceding the modal class; f2 = Frequency of the class succeeding the modal class; h = Size of class interval. c.f. = Cumulative frequency of preceding class; h = Class size]

Mode = 3 Median – 2 Mean
Median = Mode+2Mean/3
Mean = 3MedianMode/2

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