10th Maths Chapter 8 Statistics and Probability Exercise 8.1
1. Find the range and coefficient of the range of the following data.
- (i) 63, 89, 98, 125, 79, 108, 117, 68
- (ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
Solution:
Range R = L – S.
L – Largest value,
S – Smallest value.
(i) 63, 89, 98, 125, 79, 108, 117, 68.
Here L = 125
S = 63
∴ R = L – S = 125 – 63 = 62
2.If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.
Answer:
Range = 36.8
Smallest value (S) = 13.4
Range = L – S
36.8 = L – 13.4
L = 36.8 + 13.4 = 50.2
Largest value = 50.2
3. Calculate the range of the following data.
Solution:
Here the largest value = 650
The smallest value =400
∴ Range = L – S = 650 – 400
= 250
4. A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
Solution:
5. Find the variance and standard deviation of the wages of 9 workers given below:
₹ 310, ₹ 290, ₹ 320, ₹ 280, ₹ 300, ₹ 290, ₹ 320, ₹ 310, ₹ 280.
Solution:
6. A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock, and so on. How many times will it strike in a particular day? Find the standard deviation of the number of strikes the bell makes a day.
Solution:
7. Find the standard deviation of the first 21 natural numbers.
Solution:
8. If the standard deviation of data is 4.5 and if each value of the data is decreased by 5, then find the new standard deviation.
Answer:
The standard deviation of the data = 4.5
Each data is decreased by 5
The new standard deviation = 4.5
9.If the standard deviation of data is 3.6 and each value of the data is divided by 3, then find the new variance and new standard deviation.
Solution:
If the standard deviation of a data is 3.6, and each of the data is divided by 3 then the new standard deviation is also divided by 3.
∴ The new standard deviation = \(\frac{3.6}{3}\)
= 1.2
The new variance = (standard deviation)2
\(=\sigma^{2}=1.2^{2}=1.44\)
10. The rainfall recorded in various places in five districts in a week is given below.
Find its standard deviation.
Solution:
11. In a study about viral fever, the number of people affected in a town were noted as
Find its standard deviation.
Solution:
Let the assumed mean A = 35, C = 10
12. The measurements of the diameters (in cms) of the plates prepared in a factory are given below. Find its standard deviation.
Solution:
Assumed mean A = 30.5, C = 4
13. The time taken by 50 students to complete a 100-meter race are given below. Find its standard deviation.
Solution:
Assumed mean A = 11, C = 1
14. For a group of 100 candidates the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on, it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation.
Solution:
15. The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12, and 14, then find the remaining two observations.
Solution:
The given 5 numbers are 2, 4, a, b, 10, 12, and 14.
a, b are 6 and 8.
