Advertisements
Advertisements
प्रश्न
If different values of variable x are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5 and 11.1;
find
(i) the mean ` barx `
(ii) the value of ` sum (x_i - barx)`
उत्तर
(i) The given numbers are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5, 11.1
`barx` = `(x1 + x2 + x3+ x4 + x5+ .......+ xn)/ (n)`
= `( 9.8 + 5.4 + 3.7 + 1.7 + 1.8 + 2.6 + 2.8 + 8.6 + 10.5 + 11.1)/ (10 )`
= 5.8
(ii) The value of `sum_( i =1) ^ 10 ( x_i-barx)`
We know that
`sum_( i = 1)^n( x_i - barx) = (x1-barx) + (x2-barx).........+ (xn-barx) = 0`
Here
` barx ` = 5.8
Therefore
`sum_(i=1)^10 (x_i-barx)`
= ( 9.8 - 5.8) + ( 5.4 - 5.8 ) + (3.7 - 5.8 ) + ( 1.7 - 5.8 ) + ( 1.8 - 5.8 ) + (2.6 - 5.8 ) + (2.8 - 5.8 ) + ( 8.6 - 5.8 ) + ( 10.5 - 5.8 ) + ( 11.1 - 5.8 )
= 4 - 0.4 - 2.1 - 4.1 - 4 - 3.2 - 3 + 2.8 + 4.7 + 5.3
=0
APPEARS IN
संबंधित प्रश्न
Find the mean of the first six natural numbers.
In a series of tests, A appeared for 8 tests. Each test was marked out of 30 and averages 25. However, while checking his files, A could only find 7 of the 8 tests. For these, he scored 29, 26, 18, 20, 27, 24 and 29.
Determine how many marks he scored for the eighth test.
Find the mean of all factors of 10.
Find x if 9, x, 14, 18 x, x, 8, 10 and 4 have a mean of 11.
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 are 71,
find the ratio of the number of boys to the number of girls.
Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.
The mean of 5 numbers is 18. If one number is excluded, the mean of the remaining number becomes 16. Find the excluded number.
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if the observations, given above, be: divided by 2.
The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean.
If `bar"X"` is the mean of n observations x1, x2, x3,..., xn then the mean of `x_1/"a", x_2/"a", x_3/"a",...,x_"n"/"a" "is" bar"X"/"a"`, where a is an non-zero number.
i.e., if each observation is divided by a non-zero number, then the mean is also divided by it.
