In this article, we will share MP Board Class 10th Maths Book Solutions Chapter 14 Statistics Ex 14.1 Pdf, These solutions are solved subject experts from the latest edition books.

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 1
Which method did you use for finding the mean, and why?
Solution:
We can calculate the mean as follows :
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 2
∴ Mean = \(\overline{x}=\frac{\sum f_{i} x_{i}}{N}=\frac{162}{20}=8.1\)
Thus, mean number of plants per house is 8.1 Since, values of xi and fi are small, so we have used the direct method.

Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 3
Find the mean daily wages of the workers of the factory by using an appropriate method.
Solution:
Let the assumed mean, a = 150
∵ Class size, h = 20
∴ \(u_{i}=\frac{x_{i}-a}{h}=\frac{x_{i}-150}{20}\)
∴ We have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 4
Now, \(\overline{x}\) = a + h × {\(\frac{1}{N}\) Σfiui}
= 150 + 20 × \(\left(\frac{-12}{50}\right)\) = 150 – \(\frac{24}{5}\)
= 150 – 4.8 = 145.20

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 5
Solution:
Let the assumed mean, a = 18
∵ Class size, h = 2
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-18}{2}\)
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 6
⇒ [f + 44] (0) = 2[f – 20]
⇒ 2[f – 20] = 0 ⇒ f = 20
Thus, missing frequency is 20.

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.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 7
Solution:
Let the assumed mean, a = 75.5
∵ Class size, h = 3
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-75.5}{3}\)
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 8
Thus, the mean heart beats per minute is 75.9.

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 5.
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained a varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 9
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Solution:
Let the assumed mean, a = 57
∴ di = xi – 57
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 10
Thus, the average number of mangoes per box = 57.19. We choose assumed mean method.

Question 6.
The table below shows the daily expenditure on food of 25 households in a locality.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 11
Find the mean daily expenditure on food by a suitable method.
Solution:
Let the assumed mean, a = 225
∵ Class size, (h) = 50
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-225}{50}\)
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 12
Thus, the mean daily expenditure on food is ₹ 211.

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 7.
To find out the concentration of S02 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:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 13
Find the mean concentration of S02 in the air.
Solution:
Let the assumed mean, a = 0.14
∵ Class size, (h) = 0.04
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-0.14}{0.04}\)
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 14

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.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 15
Solution:
Using the direct method, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 16
Thus, mean number of days a student remained absent = 12.48.

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 17
Solution:
Let the assumed mean, a = 70
∵ Class size, (h) = 10
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-70}{10}\)
Now, we have the following table:
MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 18

MP Board Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 19
Thus, the mean literacy rate is 69.43%

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