Statistics - Algebra - Mathematics Previous Year Questions

The mean and variance of \(n\) observations \(x_1, x_2, x_3, \ldots . . x_n\) are 5 and 0 respectively. If \(\sum_{i=1}^n x_i^2=400\), then the value of \(n\) is equal to

The variance of the variates 112, 116, 120, 125 and 132 about their AM is

Which of the following set of data has least standard deviation?

If the mean of a data x is 10 and if all the observations are multiplied by 2, then the mean of new data is

For the random variable X with probability distribution is given by the table

The mean of X is

Let an angle of a triangle is 60\(^\circ\). If the variance of the angles of the triangle is 1014\(^\circ\), then the other two angles are

The mean deviation from the mean of the set of observation \(-1,0,4\) is

If the mean of the data \(p, 6,6,7,8,11,15,16\), is 3 times \(p\), then the mean deviation of the data from its mean is

The mean deviation about the mean for the following data.

$$5,6,7,8,6,9,13,12,15 \text { is }$$

If the mean deviation of the data \(1,1+d 1+2 d, \ldots, 1+100 d,(d>0)\) from their mean is 255, then '\(d\)' is equal to

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$

The coefficient of variation for the frequency distribution is

$$\begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 3 & 1 \\ \hline \boldsymbol{f}_{\boldsymbol{i}} & 1 & 3 & 5 \\ \hline \end{array}$$

Mean deviation about the mean for the following data is

$$\begin{array}{llllll} \hline \text { Class Interval } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text { Frequency } & 1 & \,2 & \,3 & \,2 & \,1 \\ \hline \end{array}$$

Based on the following statements, choose the correct option.

Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement II The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112 .

The variance of ungrouped data $2,12,3,11,5,10,6,7$, is