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 |
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.
A group of 65 students of class XI have their average height is 150.4 cm with coefficient of variation 2.5%. What is the standard deviation of their height?
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?
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 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 | 16 | 5 | 18 | 15 |
Which team is more consistent?
Find the coefficient of variation of a sample which has mean equal to 25 and standard deviation of 5
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?
Two workers on the same job show the following results:
| Worker P | Worker Q | |
| Meantime 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?
- Which worker seems to be faster in completing the job?
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?
The following table gives weights of the students of two classes. Calculate the coefficient of variation of the two distributions. Which series is more variable?
| Weight (in kg) | Class A | Class B |
| 30-40 | 22 | 13 |
| 40-50 | 16 | 10 |
| 50-60 | 12 | 17 |
Given below is the information about marks obtained in Mathematics and Statistics by 100 students in a class. Which subject shows the highest variability in marks?
| Mathematics | Statistics | |
| Mean | 20 | 25 |
| S.D. | 2 | 3 |
Select the correct option from the given alternatives :
Standard deviation of data is 12 and mean is 72 then coefficient of variation is
Answer the following :
Calculate coefficient of variation of the following data: 23, 27, 25, 28, 21, 14, 16, 12, 18, 16
Answer the following :
Calculate coefficient of variation for the data given below:
| Income (Rs.) |
3000 - 4000 | 4000 - 5000 | 5000 - 6000 | 6000 - 7000 | 7000 - 8000 | 8000 - 9000 | 9000 - 10000 |
| No. of families | 24 | 13 | 15 | 28 | 12 | 8 | 10 |
Answer the following :
Compute coefficient of variations for the following data to show whether the variation is greater in the yield or in the area of the field:
| Year | Area (in acres) |
Yield (in lakhs) |
| 2011 - 12 | 156 | 62 |
| 2012 - 13 | 135 | 70 |
| 2013 - 14 | 128 | 68 |
| 2014 - 15 | 117 | 76 |
| 2015 - 16 | 141 | 65 |
| 2016 - 17 | 154 | 69 |
| 2017 - 18 | 142 | 71 |
In a series of observations, S.D. = 5 and mean is 20, then coefficient of variation is ______.
In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is ______.
