Advertisements
Advertisements
प्रश्न
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 |
उत्तर
| C.I. | Mi value (xi) |
Frequency (fi) |
fixi | fixi2 |
| 5 – 15 | 10 | 6 | 60 | 600 |
| 15 – 25 | 20 | 7 | 140 | 2800 |
| 25 – 35 | 30 | 15 | 450 | 13500 |
| 35 – 45 | 40 | 25 | 1000 | 40000 |
| 45 – 55 | 50 | 8 | 400 | 20000 |
| 55 – 65 | 60 | 18 | 1080 | 64800 |
| 65 – 75 | 70 | 21 | 1470 | 102900 |
| Total | N = 100 | `sum"f"_"i""x"_"i"` = 4600 | `sum"f"_"i""x"_"i"^2` = 244600 |
`bar"x" = (sum"f"_"i""x"_"i")/"N" = 4600/100` = 46
Var (X) = `sigma_"x"^2`
= `1/"N" sum"f"_"i""x"_"i"^2 - (bar"x")^2`
= `1/100 xx 244600 - (46)^2`
= 2446 – 2116
= 330
S.D. = `sigma_"x"^2`
= `sqrt(330)`
= `sqrt(3.3 xx 100)`
= `10sqrt(3.3)`
= 10 × 1.8166
= 18.166
∴ C.V. = `100 xx sigma_"x"/bar"x"`
= `100 xx (18.166)/46`
= 39.49%
APPEARS IN
संबंधित प्रश्न
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)
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 |
Regarding the time required to complete the job, which worker is more consistent?
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 a larger variability in wages?
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 |
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?
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 |
Find the coefficient of variation of a sample which has mean equal to 25 and standard deviation of 5
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?
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 the coefficient of variation for the data given below:
| Size (cm) | 5 - 8 | 8 - 11 | 11 - 14 | 14 - 17 | 17 - 20 | 20 - 23 | 23 - 26 |
| No of items | 3 | 14 | 13 | 16 | 19 | 24 | 11 |
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 |
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 ______.
In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is ______.
