# 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)

#### 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]

#### APPEARS IN

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

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