Let x¯ be the mean of x1, x2, ..., xn and y the mean of y1, y2, ..., yn. If z is the mean of x1, x2, ..., xn, y1, y2, ..., yn, then z is equal to ______. - Mathematics

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Let `barx` be the mean of x1, x2, ..., xn and y the mean of y1, y2, ..., yn. If z is the mean of x1, x2, ..., xn, y1, y2, ..., yn, then z is equal to ______.

Options

  • `barx + bary`

  • `(barx + bary)/2`

  • `(barx + bary)/n`

  • `(barx + bary)/(2n)`

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Solution

Let `barx` be the mean of x1, x2, ..., xn and y the mean of y1, y2, ..., yn. If z is the mean of x1, x2, ..., xn, y1, y2, ..., yn, then z is equal to `(barx + bary)/2`.

Explanation:

Given, `sum_(i = 1)^n  x_i = nbarx` and `sum_(i = 1)^n y_i = nbary`  .....(i) `[because 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)`

= `(barx + bary)/2`  ......[From equation (i)]

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Chapter 14: Statistics & Probability - Exercise 14.1 [Page 133]

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NCERT Exemplar Mathematics Class 9
Chapter 14 Statistics & Probability
Exercise 14.1 | Q 15 | Page 133

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