Advertisements
Advertisements
प्रश्न
The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?
Advertisements
उत्तर
Let x1, x2, x3,..., x16 be 16 numbers with their mean equal to 8. Then
`bar"X" = (1)/"n" (sum_(i = 1)^16 x_i)`
⇒ 8 = `(x_1 + x_2 + ... + x_16)/(16)`
⇒ x1 + x2 + ... + x16 = 16 x 8 = 128 ...(i)
New numbers are x1 + x2 + 2, x3 + 2,..., x16 + 2.
Let `bar"X"` be the mean of new numbers. Then,
`bar"X" = ((x_1 + 2) + (x_2 + 2) + ... (x_16 + 2))/(16)`
= `((x_1 + x_2 + ... + x_16) + 2 xx 16)/(16)`
= `(128 + 32)/(16)`, ...[Using (i)]
= `(160)/(16)`
= 10.
संबंधित प्रश्न
Find the mean of the first six natural numbers.
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.
The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88.
Find the correct mean.
If the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11,
find:
(i) The value of x;
(ii) The mean of first three observations.
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 monthly salary of 10 members of a group is Rs.1,445, one more member whose monthly salary is Rs.1,500 has joined the group. Find the mean monthly salary of 11 members of the group.
The mean of 100 items was found to be 30. If at the time of calculation two items were wrongly taken as 32 and 12 instead of 23 and 11, 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.
