Advertisements
Advertisements
Question
The algebraic sum of the deviations of a set of n values from their mean is
Options
0
n − 1
n
n + 1
Solution
If `bar( X) `be the mean of the n observations q `X_i,...,X_n`, then we have
`bar(X) = 1/nsum_(i=1)^n X_i`
`⇒ sum_(i=1)^n X_i = nbar(X)`
Let ` bar(X)` be the mean of n values `X_i,...,X_n` . So, we have
`bar(X) = 1/nsum_(i=1)^n X_i`
`⇒ sum_(i=1)^n X_i = nbar(X)`
The sum of the deviations of n values `X_i,...,X_n` from their mean`bar(X)` is
`(x_1 - bar(X) ) +(x_2 - bar(X) )+......+(x_n-bar(X))`
`= sum_(i=1)^n(x_i- bar(X))`
`= sum_(i=1)^n x_i- sum_(i=1)^n bar(X)`
`= nbar(X) - nbar(X)`
=0
APPEARS IN
RELATED QUESTIONS
Find the mean of 994, 996, 998, 1002 and 1000.
The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6
of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.
Calculate the mean for the following distribution:
| x : | 5 | 6 | 7 | 8 | 9 |
| f : | 4 | 8 | 14 | 11 | 3 |
The mean of the following data is 20.6. Find the value of p.
| x : | 10 | 15 | p | 25 | 35 |
| f : | 3 | 10 | 25 | 7 | 5 |
Find the mean of the following distribution:
| x : | 10 | 12 | 20 | 25 | 35 |
| F : | 3 | 10 | 15 | 7 | 5 |
Find the mode from the following data:
125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125
If the mean of 2, 4, 6, 8, x, y is 5, then find the value of x + y.
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is ______.
Obtain the mean of the following distribution:
| Frequency | Variable |
| 4 | 4 |
| 8 | 6 |
| 14 | 8 |
| 11 | 10 |
| 3 | 12 |
The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
