Advertisements
Advertisements
प्रश्न
Answer the following :
Find variance and S.D. for the following set of numbers: 125, 130, 150, 165, 190, 195, 210, 230, 245, 260
Advertisements
उत्तर
| xi | `x_"i" - barx` | `(x_"i" - barx)^2` |
| 125 | – 65 | 4225 |
| 130 | – 60 | 3600 |
| 150 | – 40 | 1600 |
| 165 | – 25 | 625 |
| 190 | 0 | 0 |
| 195 | 5 | 25 |
| 210 | 20 | 400 |
| 230 | 40 | 1600 |
| 245 | 55 | 3025 |
| 260 | 70 | 4900 |
| `sumx_"i"` = 1900 | `sum(x_"i" - barx)^2` = 20000 |
Here, n = 10
`bar(x) = (sumx_"i")/"n" = 1900/10` = 190
Var (X) = `sigma_x^2 = 1/"n" sum(x_"i" - barx)^2 = 20000/10` = 2000
S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(2000)`
= 44.72
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
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 |
Following data gives age of 100 students in a college. Calculate variance and S.D.
| Age (In years) | 16 | 17 | 18 | 19 | 20 | 21 |
| No. of Students | 20 | 7 | 11 | 17 | 30 | 15 |
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 |
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 :
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 :
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 :
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 ______
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 ______.
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` = ______.
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If α and `sqrtβ` are the mean and standard deviation respectively for correct data, then (α, β) 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 ______.
The mean of a set of observation is `overlinex`. If each observation is divided by α, α ≠ 0 and then is increased by 10, then the mean of the new set is ______.
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:
