Advertisements
Advertisements
Question
Let `barx` be the mean of x1, x2, ..., xn and `bary` the mean of y1, y2, ..., yn. If `barz` is the mean of x1, x2, ..., xn, y1, y2, ..., yn, then `barz` is equal to ______.
Options
`barx + bary`
`(barx + bary)/2`
`(barx + bary)/n`
`(barx + bary)/(2n)`
Solution
Let `barx` be the mean of x1, x2, ..., xn and `bary` the mean of y1, y2, ..., yn. If `barz` is the mean of x1, x2, ..., xn, y1, y2, ..., yn, then `barz` is equal to `underlinebb((barx + bary)/2)`.
Explanation:
Given, `sum_(i = 1)^n x_i = nbarx` and `sum_(i = 1)^n y_i = nbary` ...(i) `[∵ barx = (sum_(i = 1)^n x_i)/n]`
Now, `barz = ((x_1 + x_2 + ... + x_n) + (y_1 + y_2 + ... + y_n))/(n + n)`
= `(sum_(i = 1)^n x_i + sum_(i = 1)^n y_i)/(2n)`
= `(nbarx + nbary)/(2n)` ...[From equation (i)]
= `(barx + bary)/2`
APPEARS IN
RELATED QUESTIONS
Explain, by taking a suitable example, how the arithmetic mean alters by
(i) adding a constant k to each term
(ii) subtracting a constant k from each them
(iii) multiplying each term by a constant k and
(iv) dividing each term by a non-zero constant k.
The sums of the deviations of a set of n values 𝑥1, 𝑥2, … . 𝑥11 measured from 15 and −3 are − 90 and 54 respectively. Find the valùe of n and mean.
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 missing frequency (p) for the following distribution whose mean is 7.68.
| x | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | p | 8 | 4 |
Find the missing frequencies in the following frequency distribution if its known that the mean of the distribution is 50.
| x | 10 | 30 | 50 | 70 | 90 | |
| f | 17 | f1 | 32 | f2 | 19 | Total =120 |
If the median of the scores 1, 2, x, 4, 5 (where 1 < 2 < x < 4 < 5) is 3, then find the mean of the scores.
The mean of n observations is X. If k is added to each observation, then the new mean is
For which set of numbers do the mean, median and mode all have the same value?
If the mean of the following data is 20.2, find the value of p:
| x | 10 | 15 | 20 | 25 | 30 |
| f | 6 | 8 | p | 10 | 6 |
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.
