Gujarat Board Solutions Class 10 Maths Chapter 14 Statistics

 Gujarat Board Solutions Class 10 Maths Chapter 14 Statistics

Gujarat Board Textbook Solutions Class 10 Maths Chapter 14 Statistics

Ex 14.1

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

Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.

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.

Question 4.
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heartbeat per minute for these women, choosing a suitable method.

Question 5.
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying numbers of mangoes. The following was the distribution of mangoes according to the number of boxes.

Question 6.
The table below shows the daily expenditure on the food of 25 households in a locality.

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 n city and is presented below. Find the mean concentration of SO2 in the air.

Question 8.
A class teacher has the following absent record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Solution:

Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Solution:

Ex 14.2

Question 1.
The following table shows the ages of the patients admitted in a hospital for a year.

Question 2.
The following data gives information on the observed lifetimes (in hours) of 225 electrical components.

Question 3.
The following date gives the distribution of total monthly expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

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:
Mode: Since the maximum number of states/UT have the number of students per teacher in the interval 30-35, the modal class is 30-35.
Therefore, l = 30, h = 5, f1 = 10, f0= 9, f2 = 3

Question 5.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Question 6.
A student noted in 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:

Ex 14.3

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.

 

Question 2.
If the median of the distribution given below is 28.5, find the values of x and y. ∑fi = 60.

Question 3.
A life insurance agent found the following data for the distribution of ages of 100 policyholders. Calculate the median age, if polices are only given to persons having age 18 years onwards but less than 60 years.

Solution:

Question 4.
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Find the median length of the leaves.
Solution:
Firstly, data needs to be converted into continuous classes.

Question 5.
The following table gives the distribution of the lifetime of 400 neon lamps..

Find the median lifetime of a lamp.
Solution:

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 alphabets in the surnames was obtained as follows:

 

Question 7.
The distribution below gives the weights of 30 students of a class, find the median weight of the students.

Ex 14.4

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 it so give.
Solution:
Less than type cumulative frequency distribution.

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:
Here, n/2 = 35/2 = 17.5
Locate 17.5 on the y-axis. From this point, draw a line parallel to the x-axis cutting the curve at a point. From this point, draw a perpendicular to the x-axis. The point of intersection of this perpendicular with the x-axis determines the median of the given data as 46.5 kg. Median weight by using the formula Grouped Frequency Distribution


Now, n = 35
So, n/2 = 35/2 = 17.5
This observation lies in class 46 – 48.
So, 46 – 48 is the median class.
Therefore, l = 46, h = 2, f= 14, c.f = 14
∴ Median (by using formula)
= 46 + [17.5–14/14 x 2
= 46 + 1/2 = 46.5 kg.
Verification: We find that the median weight obtained from the graph is the same as the median weight obtained by using the formula.

Question 3.
The following table gives production yield per hectare of wheat of loo farms of a village.

Change the distribution to a more than type distributIon, and draw its ogive.
Solution:

More than type of distribution.