Advertisements
Advertisements
Question
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.
Solution
(i) Given that the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11.
Mean = `"Observations"/n`
11 = `[ x + x + 2 + x + 4 + x + 6 + x + 8]/5`
11 = `[ 5x + 20 ]/5`
x = `35/5`
x = 7
(ii)The mean of first three observations are
= `[ x + x + 2 + x + 4 ]/3`
= `[ 3x + 6 ]/3`
= `[ 3 xx 7 + 6 ]/3` .....[ Since x = 7 ]
= `[ 21 + 6 ]/3`
= 9.
APPEARS IN
RELATED QUESTIONS
Find the mean of 43, 51, 50, 57 and 54.
Find the mean of the first ten odd 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 weight of 120 students of a school is 52.75 kg. If the mean weight of 50 of them is 51 kg,
find the mean weight of the remaining students.
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 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.
The mean of 100 observations is 40. It is found that an observation 53 was misread as 83.
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.
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.
