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.
Which method did you use for finding the mean, and why?
Solution:
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Ex 14.1 Class 10 Maths Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
Find the mean daily wages of the workers of the factory by using an appropriate method.
Solution:
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.
Solution:
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
Solution:
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.
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 Question 6.
The table below shows the daily expenditure on food of 25 households in a locality.
Find the mean daily expenditure on food by a suitable method.
Solution:
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:
Find the mean concentration of SO2 in the air.
Solution:
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.
Solution:
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.
Solution:
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
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:
(i) Direct method:
where ‘fi‘ is the frequency corresponding to the class mark ‘xi‘
(ii) Assumed mean method:
Where A is assumed mean and di = xi – A
(iii) step deviation method:
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:
l =lower limit of the modal class,
f1 = frequency of the modal class
f 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
If number of data n is even, then the median is the average of
(ii) For Grouped Data:
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)
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
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
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 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.
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Solution:
Ex 14.2 Class 10 Maths Question 2.
The following data gives information on the observed lifetimes (in hours) of 225 electrical components:
Determine the modal lifetimes of the components.
Solution:
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:
Solution:
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.
Solution:
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.
Find the mode of the data.
Solution:
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:
Solution:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.3
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 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.
Solution:
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.
Solution:
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.
Solution:
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:
Find the median length of the leaves.
Solution:
Ex 14.3 Class 10 Maths Question 5.
The following table gives the distribution of the lifetime of 400 neon lamps:
Find the median lifetime of a lamp.
Solution:
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:
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:
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.
Solution:
NCERT Solutions For Class 10 Maths Chapter 14 Statistics Ex 14.4
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 14 Statistics Exercise 14.4.
Ex 14.4 Class 10 Maths Question 1.
The following distribution gives the daily income of 50 workers of a factory.
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Solution:
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:
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 Question 3.
The following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution, and draw its ogive.
Solution:
