If mean of the series \(x_1\), \(x^2\), ….. , \(x_n\) is \(\bar{x}\), then the mean of the series \(x_i\) + 2i, i = 1, 2, ……, n will be

Solution :

As given \(\bar{x}\) = \(x_1 + x_2 + …. + x_n\over n\)

If the mean of the series \(x_i\) + 2i, i = 1, 2, ….., n be \(\bar{X}\), then

\(\bar{X}\) = \((x_1+2) + (x_2+2.2) + (x_3+2.3) + …. + (x_n + 2.n)\over n\)

= \(x_1 + x_2 + …. + x_n\over n\) + \(2(1+2+3+….+n)\over n\)

= \(\bar{x}\) + \(2n(n+1)\over 2n\)

= \(\bar{x}\) + n + 1.


Similar Questions

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is

The mean and the variance of a binomial distribution are 4 and 2, respectively. Then, the probability of 2 success is

In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

Leave a Comment

Your email address will not be published.