Advertisements
Advertisements
प्रश्न
The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?
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.
APPEARS IN
संबंधित प्रश्न
Find the mean of 43, 51, 50, 57 and 54.
Find the mean of the first six natural numbers.
Find the mean of the first ten odd natural numbers.
Find the mean of all factors of 10.
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 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)`
The mean of 5 numbers is 18. If one number is excluded, the mean of the remaining number becomes 16. Find the excluded number.
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.
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.
