Advertisements
Advertisements
Question
The following table gives weights of the students of class A. Calculate the Coefficient of variation. `("Given": sqrt0.8 = 0.8944)`
| Weight (in kg) | Class A |
| 25 – 35 | 8 |
| 35 – 45 | 4 |
| 45 – 55 | 8 |
Advertisements
Solution
| Weight (in kg) |
Class A (fi) |
Mid value (xi) |
fixi | fixi2 |
| 25 – 35 | 8 | 30 | 240 | 7200 |
| 35 – 45 | 4 | 40 | 160 | 6400 |
| 45 – 55 | 8 | 50 | 400 | 20000 |
| Total | N = 20 | ∑fixi = 800 | ∑fixi2 = 33600 |
`bar"x" = (sum"f"_"i""x"_"i")/"N"`
= `(800)/(20)`
= 40
Var(X) = `sigma_"x"^2=(sum"f"_"i""x"_"i"^2)/"N"-(bar"x")^2`
= `33600/20-(40)^2`
= 1680 − 1600
= 80
∴ S.D. = σx = `sqrt80`
= `sqrt((100xx8)/10)`
= `10sqrt0.8 `
= 10(0.8944)
= 8.944
C.V. (X) = `sigma_"x"/bar"x" xx 100`
= `(8.944)/(40) xx 100`
= 22.36%
APPEARS IN
RELATED QUESTIONS
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10.
(Given: `sqrt8` = 2.8284)
Find the coefficient of Variation of a sample which has mean equal to 25 and standard deviation of 5.
Two workers on the same job show the following results:
|
Worker P |
Worker Q | |
| Mean time for completing the job (hours) | 33 | 21 |
| Standard Deviation (hours) | 9 | 7 |
Regarding the time required to complete the job, which worker is more consistent?
Two workers on the same job show the following results:
| Worker P | Worker Q | |
| Mean time for completing the job (hours) | 33 | 21 |
| Standard Deviation (hours) | 9 | 7 |
Which worker seems to be faster in completing the job?
Given below is the information about marks obtained in Mathematics and Statistics by 100 students in a class. Which subject shows A the highest variability in marks?
| Mathematics | Statistics | |
| Mean | 20 | 25 |
| S.D. | 2 | 3 |
The mean and standard deviations of two brands of watches are given below:
| Brand-I | Brand-II | |
| Mean | 36 months | 48 months |
| S.D. | 8 months | 10 months |
Calculate a coefficient of variation of the two brands and interpret the results.
Calculate coefficient of variation for the data given below [Given : `sqrt(3.3)` = 1.8166]
| C.I. | 5 – 15 | 15 – 25 | 25 – 35 | 35 – 45 | 45 – 55 | 55 – 65 | 65 – 75 |
| f | 6 | 7 | 15 | 25 | 8 | 18 | 21 |
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82
A group of 65 students of class XI have their average height is 150.4 cm with coefficient of variance 2.5%. What is the standard deviation of their height?
A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively: Which department has a larger bill?
A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively: Which department has larger variability in wages?
Compute coefficient of variation for team A and team B:
| No. of goals | 0 | 1 | 2 | 3 | 4 |
| No. of matches played by team A | 19 | 6 | 5 | 16 | 14 |
| No. of matches played by team B | 16 | 14 | 10 | 14 | 16 |
Which team is more consistent?
Answer the following :
Calculate coefficient of variation of the following data: 23, 27, 25, 28, 21, 14, 16, 12, 18, 16
Answer the following :
Following data relates to the distribution of weights of 100 boys and 80 girls in a school:
| Boys | Girls | |
| Mean | 60 | 47 |
| Variance | 16 | 9 |
Which of the two is more variable?
Answer the following :
There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies are taken and the average running life (in years) is recorded
| Life (in years) | No of Cars | |
| Company U | Company V | |
| 0 - 5 | 5 | 14 |
| 5 - 10 | 18 | 8 |
| 10 - 15 | 17 | 18 |
Which company shows greater consistency?
In a series of observations, S.D. = 5 and mean is 20, then coefficient of variation is ______.
