Advertisements
Advertisements
प्रश्न
Compute the variance and S.D.
| X | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| Frequency | 15 | 12 | 10 | 8 | 9 | 10 | 6 |
उत्तर
We prepare the following table to compute variance and S.D.:
| xi | fi | ui = xi – A A = 34 |
fiui | fiui2 = fiui × ui |
| 31 | 15 | – 3 | – 45 | 135 |
| 32 | 12 | – 2 | – 24 | 48 |
| 33 | 10 | – 1 | – 10 | 10 |
| 34 | 8 | 0 | 0 | 0 |
| 35 | 9 | 1 | 9 | 9 |
| 36 | 10 | 2 | 20 | 40 |
| 37 | 6 | 3 | 18 | 54 |
| `sumf_"i"` = 70 | `sumf_"i"u_"i"` = – 32 | `sumf_"i"u_"i"^2` = 296 |
From the table, `sumf_"i"u_"i" = -32, sumf_"i" = 70, sumf_"i"u_"i"^2` = 296
∴ `bar(u) = (sumf_"i"u_"i")/(sumf_"i") = (-32)/70` = – 0.4571
`sigma_u^2 = (sumf_"i"u_"i"^2)/(sumf_"i") - (baru)^2 = 296/70 - (-0.4571)^2`
= 4.2286 – 0.2089 = 4.0197
∴ Var (x) = `sigma_x^2 = sigma_u^2` = 4.0197
S.D. = `sigma_x = sqrt(4.0197)` = 2.005
Hence, variance = 4.0197 and S.D. = 2.005
APPEARS IN
संबंधित प्रश्न
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
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 |
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 :
The positive square root of the mean of the squares of the deviations of observations from their mean is called:
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:
25, 21, 23, 29, 27, 22, 28, 23, 21, 25
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 |
The S.D. and C.V. for the following frequency distribution is
| xi | 60 | 61 | 62 | 63 | 64 | 65 | 66 |
| fi | 3 | 10 | 11 | 13 | 7 | 5 | 1 |
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 standard deviation of the data 8, 7, 1, 15, 14, 10, 12 is ______.
For certain data, the following information is available. Obtain the combined standard deviation.
| X | Y | |
| Mean | 13 | 17 |
| S.D. | 3 | 2 |
| Size | 20 | 30 |
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` = ______.
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 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 ______.
