Advertisements
Advertisements
Question
Find the variance and S.D. of the following frequency distribution which gives the distribution of 200 plants according to their height:
| Height (in cm) | 14 – 18 | 19 – 23 | 24 – 28 | 29 – 33 | 34 – 38 | 39 – 43 | 44 – 48 |
| No. of plants | 5 | 18 | 44 | 70 | 36 | 22 | 5 |
Solution
Since data is not continuous, we have to make it continuous.
Let u = `(x - "A")/"h" = (x - 31)/5`
Calculation of variance of u:
| Height (in cm) C. I. |
Mid value (xi) | No. of plants (fi) | ui = `(x_"i" - 31)/5` | fiui | fiui2 |
| 13.5 – 18.5 | 16 | 5 | – 3 | – 15 | 45 |
| 18.5 – 23.5 | 21 | 18 | – 2 | – 36 | 72 |
| 23.5 – 28.5 | 26 | 44 | – 1 | – 44 | 44 |
| 28.5 – 33.5 | 31 | 70 | 0 | 0 | 0 |
| 33.5 – 38.5 | 36 | 36 | 1 | 36 | 36 |
| 38.5 – 43.5 | 41 | 22 | 2 | 44 | 88 |
| 43.5 – 48.5 | 46 | 5 | 3 | 15 | 45 |
| N = 200 | `sumf_"i"u_"i"` = 0 | `sumf_"i"u_"i"^2` = 330 |
`bar(u) = (sumf_"i"u_"i")/"n" = 0/200` = 0
Var (u) = `sigma_u^2 = (sumf_"i"u_"i"^2)/"n" - (baru)^2`
= `330/200 - 0^2`
= 1.65
∴ Var (X) = h2 Var (u) = (5)2 × 1.65 = 25 × 1.65 = 41.25
∴ S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(41.25)`
= 6.42
APPEARS IN
RELATED QUESTIONS
Find variance 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, 2, 6
Find variance 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 | 12 | 14 | 16 | 18 | 20 |
| F | 8 | 10 | 10 | 7 | 6 | 4 | 3 | 4 | 2 | 6 |
Compute the variance and S.D.
| X | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| Frequency | 15 | 12 | 10 | 8 | 9 | 10 | 6 |
Find mean, variance and S.D. of the following data:
| Classes | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| Frequency | 7 | 14 | 6 | 13 | 9 | 15 | 11 | 10 | 15 |
The mean of 5 observations is 4.8 and the variance is 6.56. If three of the five observations are 1, 3 and 8, find the other two observations
Select the correct option from the given alternatives :
The standard deviation of a distribution divided by the mean of the distribution and expressing in percentage is called:
Select the correct option from the given alternatives :
If the S.D. of first n natural numbers is `sqrt(2)`, then the value of n must be ––––––.
Select the correct option from the given alternatives :
For any two numbers, SD is always
Answer the following :
Find variance and S.D. for the following set of numbers: 125, 130, 150, 165, 190, 195, 210, 230, 245, 260
Answer the following :
Following data gives no. of goals scored by a team in 100 matches. Compute the standard deviation
| No. of Goals Scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 5 | 20 | 25 | 15 | 20 | 5 |
Answer the following :
Compute the variance and S.D. for the following data:
| X | 62 | 30 | 64 | 47 | 63 | 46 | 35 | 28 | 60 |
| F | 5 | 8 | 3 | 4 | 5 | 7 | 8 | 3 | 7 |
Answer the following :
Given below is the frequency distribution of marks obtained by 100 students. Compute arithmetic mean and S.D.
| Marks | 40 - 49 | 50 - 59 | 60 - 69 | 70 - 79 | 80 - 89 | 90 - 99 |
| No. of students | 4 | 12 | 25 | 28 | 26 | 5 |
Find the Standard Deviation of the following data: 14, 22, 9, 15, 20, 17, 12, 11.
The mean and S.D. of the scores of 100 candidates were found to be 80 and 15 respectively. Later, it was discovered that a score of 50 was wrongly read as 40. The correct mean and S.D. respectively are ______
Coefficients of variation of two distributions are 30 and 40 and their arithmetic means are 10 and 25 respectively. The difference of their standard deviations is ______
The S.D. of 20 items is 15 and if each item is decreased or increased by 1, then standard deviation will be ______.
The standard deviation of the data 8, 7, 1, 15, 14, 10, 12 is ______.
If the S.D. of the data 1, 2, 4, 5, 6, 7, 9 is 2.59, then the S.D. of 3, 6, 12, 15, 18, 21, 27 is ______.
The mean and standard deviation of random variable X are 10 and 5 respectively, then `"E"(("X" - 15)/5)^2` = ______.
Consider three observations a, band c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
If the mean of the data 7, 7, 9, 7, 8, 7, λ, 8 is 7, then the variance of this data is ______.
The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be ______.
The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ______.
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to ______.
Let x1, x2 ,..., xn be n observations such that `sumx_1^2` = 400 and `sumx_i` = 80. Then, a possible value of n among the following is:
The variance of first n natural numbers is ______.
