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प्रश्न
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 ______.
विकल्प
`barx + bary`
`(barx + bary)/2`
`(barx + bary)/n`
`(barx + bary)/(2n)`
उत्तर
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`
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