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NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

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NCERT TEXTBOOK QUESTIONS SOLVED
EXERCISE 14.1

Page No. 270
Q 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: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Which method did you use for finding the mean, and why?
Sol. We can calculate the mean as:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

⇒  NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, mean number of plants per house is 8.1.
Since, values of xi and fi are small
∴ We have used the direct method.

Q 2. Consider the following distribution of daily wages of 50 workers of a factory. 
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Find the mean daily wages of the workers of the factory by using an appropriate method.
Sol. 
To find the class mark for each interval, the following relation is used.
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

Class size (h) of this data = 20
taking 550 as assured mean (a), di, uj and fiuj can be calculated as follows.
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
From the table, it can be observed that
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Therefore, the mean daily wage of the workers of the factory is Rs 545.20

Q 3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Sol. Let the assumed mean, a = 16
∵ Class interval h = 2
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Now, we have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Since  NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
∴   NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

⇒  NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

⇒  NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
⇒ f + 44 = 2 (f + 12) = 2f + 24
⇒− f = −44 + 24 = −20
⇒ f = 20
Thus, the missing frequency is 20.

Page No. 271
Q 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: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Sol. Let the assumed mean a = 75.5
∴ Class interval h = 3
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Now, we have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, the mean heart beat per minute is 75.9.

Q 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: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose ?
Sol. Let the assumed mean a = 60
Here, Class interval h = 3
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Now, we have the following table:

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, the average number of mangoes per box = 57.19.

Q 6. The table below shows the daily expenditure on food of 25 households in a locality.
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Find the mean daily expenditure on food by a suitable method.
Sol. Let the assumed mean, a = 225
And class interval h = 50
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
∴ We have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, the mean daily expenditure of food is Rs 211.

Q 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: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Find the mean concentration of SO2 in the air.
Sol. Let the assumed mean a = 0.14
Here, class interval h = 0.04
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
∴ We have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, mean concentration of SO2 in air is 0.099 ppm.

Page No. 272
Q 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: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Sol. Using the direct method, we have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, mean number of days a student remained absent = 12.48. (Approx.)

Q 9. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Sol. Let  assumed mean a =70
∴ Class interval h =10
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Now, we have the following table:
NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10

NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10
Thus, the mean literacy rate is 69.43%.

The document NCERT Solutions: Statistics (Exercise 14.1) Notes | Study Mathematics (Maths) Class 10 - Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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