# Statistics - Solved Questions and answers

1). If the sum of 11 consecutive natural numbers is 2761, then the middle number is:
 A). 249 B). 250 C). 251 D). 252
2). The mean weight of 9 items is 15. If one more item is added to the series, the mean 16. The value of 10th item is
 A). 35 B). 30 C). 25 D). 20
3). The average of the square of the number 0, 1, 2, 3, 4.........n is:
 A). $$\Large \frac{1}{2}n \left(n+1\right)$$ B). $$\Large \frac{1}{6}n \left(2n+1\right)$$ C). $$\Large \frac{1}{6} \left(n+1\right) \left(2n+1\right)$$ D). $$\Large \frac{1}{6}n \left(n+1\right)$$
4). If the average of number 148, 146, 144, 142,..... in AP be 125, then the total numbers in the series will be
 A). 18 B). 24 C). 30 D). 48
5). The mean of the values of 1, 2, 3, ..., n with respectively frequencies x, 2x, 3x, ..., nx is
 A). $$\Large \frac{n}{2}$$ B). $$\Large \frac{1}{3} \left(2n+1\right)$$ C). $$\Large \frac{1}{6} \left(2n+1\right)$$ D). $$\Large \frac{n}{3}$$

6). The mean of 12 items is $$\Large \bar{X}$$ . If the first term is increased by 1, second by 2 and so on, then the new mean is
 A). $$\Large \overline{X}+n$$ B). $$\Large \overline{X}+\frac{n}{2}$$ C). $$\Large \overline{X}+\frac{n+1}{2}$$ D). none of these
7). If the mean of n observation $$\Large 1^{2},\ 2^{2},\ 3^{2},........n^{2}$$, is $$\Large \frac{46}{11}n$$, then n is equal to
 A). 11 B). 12 C). 23 D). 22
8). In a moderately skewed distribution the values of mean and median are 5 and 6 respectively. The value of mode in such a situation is approximately equal to:
 A). 8 B). 11 C). 16 D). none of these
9). The value of mean, median and mode coincides, then the distribution is
 A). Positive skewness B). Symmetrical distribution C). Negative skewness D). All of these
10). The algebraic sum of the deviation of 20 observations measured from 30 is 2. Then mean of observations is
 A). 28.5 B). 30.1 C). 30.5 D). 29.6
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