Advertisements
Advertisements
प्रश्न
Compute the variance and S.D.
| x | 1 | 3 | 5 | 7 | 9 |
| Frequency | 5 | 10 | 20 | 10 | 5 |
उत्तर
We prepare the following table for the calculation of variance and S.D.:
| xi | fi | fixi | fixi2 |
| 1 | 5 | 5 | 5 |
| 3 | 10 | 30 | 90 |
| 5 | 20 | 100 | 500 |
| 7 | 10 | 70 | 490 |
| 9 | 5 | 45 | 405 |
| Total | N = 50 | ∑fixi = 250 | ∑fixi2 = 1490 |
`bar"x"=(∑"f"_"i""x"_"i")/"N"=250/50` = 5
Var(X) = `σ_"x"^2=(∑"f"_"i""x"_"i"^2)/"N"-(bar"x")^2`
= `(1490)/(50) - (5)^2`
= 29.8 – 25
= 4.8
∴ S.D, σx = `sqrt("Var"("X"))=sqrt4.8`
APPEARS IN
संबंधित प्रश्न
Find the various and S.D. for the following set of numbers.
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6
Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129
Compute variance and standard deviation for the following data:
| x | 2 | 4 | 6 | 8 | 10 |
| f | 5 | 4 | 3 | 2 | 1 |
Following data gives age of 100 students in a school. Calculate variance and S.D.
| Age (In years) | 10 | 11 | 12 | 13 | 14 |
| No. of students | 10 | 20 | 40 | 20 | 10 |
The mean and variance of 5 observations are 3 and 2 respectively. If three of the five observations are 1, 3 and 5, find the values of other two observations.
Obtain standard deviation for the following date:
| Height (in inches) | 60 – 62 | 62 – 64 | 64 – 66 | 66 – 68 | 68 – 70 |
| Number of students | 4 | 30 | 45 | 15 | 6 |
The following distribution was obtained change of origin and scale of variable X.
| di | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| fi | 4 | 8 | 14 | 18 | 20 | 14 | 10 | 6 | 6 |
If it is given that mean and variance are 59.5 and 413 respectively, determine actual class intervals.
Find variance and S.D. for the following set of numbers.
25, 21, 23, 29, 27, 22, 28, 23, 27, 25
(Given `sqrt(6.6)` = 2.57)
Following data gives no. of goals scored by a team in 100 matches:
| No. of goals scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 15 | 20 | 25 | 15 | 20 | 5 |
Compute the variance and standard deviation for the above data.
