Statistics and Probability Ex 8.2-10th Std Maths-Book Back Question And Answer
Question 1.
The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.
Answer:
Standard deviation of a data (σ) = 6.5
Mean of the data (x¯) = 12.5
Coefficient of variation = σx¯×100%
= 6.512.5×100%=52%
Coefficient of variation = 52%
Question 2.
The standard deviation and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.
Answer:
Standard deviation (σ) = 1.2
Coefficient of variation = 25.6
Question 3.
If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.
Answer:
Mean (x¯) = 15
Co efficient of variation = 48
Question 4.
If n = 5, x¯ = 6, Σx2 = 765, then calculate the coefficient of variation.
Answer:
Question 5.
Find the coefficient of variation of 24, 26, 33, 37, 29, 31.
Answer:
Arrange in ascending order we get 24, 26, 29, 31, 33, 37
Assumed mean = 29
Question 6.
The time taken (in minutes) to complete homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.
Answer:
Arrange in ascending order we get, 38, 40, 43, 44, 46, 47, 49, 53.
Assumed mean = 46
= 45345%
= 10.066
Coefficient of variation = 10.07%
Question 7.
The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation of 4.6 and 2.4 respectively. Who is more consistent in performance?
Answer:
Total marks scored by sathya = 460
Total marks scored by vidhya = 480
Number of subjects = 5
Mean marks of sathya = 4605
x¯ = 92%
Given standard deviation, (σ) = 4.6
Vidhya coefficient of variation is less than Sathya.
Vidhya is more consistent.
Question 8.
The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below.
Which of the three subjects shows the highest variation and which shows the lowest variation in marks?
Answer:
(i) Mathematics:
Mean (x¯) = 56
Standard deviation (σ) = 12
Coefficient variation (CV1) = σx¯×100=1256×100
Science shows the highest variation
Social science shows the lowest variation
Question 9.
The temperature of two cities A and B in the winter season are given below.
Find which city is more consistent in temperature changes?
Answer:
(i) city A:
Assumed mean = 22
C.V of city A < C.V of city B
City A is more consistent in temperature change.
