List of top Mathematics Questions on Measures of Dispersion

Consider a data consisting of 10 observations \[ x_1, x_2, \dots, x_{10}, \] whose mean is \(5\) and variance is \(7\). If the mean and the variance of the first 8 observations \[ x_1, x_2, \dots, x_8 \] are \(4\) and \(3.5\), respectively, and \[ x_9<x_{10}, \] then the value of \[ 3x_9 + 2x_{10} \] is:

The mean deviation about the mean for the following data is \[ \begin{array}{c|cccc} x_i & 1 & 2 & 4 & 7\\ \hline f_i & 3 & 2 & 4 & 1 \end{array} \]

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is 255, then $d =$

The variance of the first $n$ even natural numbers is:

If \( \sum_{i=1}^{9} (x_i - 5) = 9 \) and \( \sum_{i=1}^{9} (x_i - 5)^2 = 45 \), then the standard deviation of the 9 items \(x_1, x_2, \ldots, x_9\) is:

If \( \sum_{i=1}^{10} (x_i - 3) = 7 \) and \( \sum_{i=1}^{10} (x_i - 3)^2 = 27 \), then the standard deviation of the 10 items is

Let $x_1, x_2, \ldots, x_n$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ is

The mean square deviation of a set of observations \(x_1,x_2,\ldots,x_n\) about point \(c\) is defined as \[ \frac1n\sum_{i=1}^n(x_i-c)^2. \] The mean square deviations about \(-2\) and \(2\) are 18 and 10 respectively. The standard deviation of the set of observations is