List of top Mathematics Questions on Statistics

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are \( 2, 3, 5, 10, 11, 13, 15, 21 \), then the mean deviation about the median of all the 10 observations is:

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become $10.1$ and $1.99$, respectively. Then $\alpha+\beta$ equals

Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :

If the mean deviation about the median of the numbers \[ k,\,2k,\,3k,\,\ldots,\,1000k \] is \(500\), then \(k^2\) is equal to

If the median of the following distribution is 32.5, then find the values of x and y.

Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

Find mean and mode of the following frequency distribution :

The median of the following data is 32.5, find the missing frequencies \(x\) and \(y\) :

If for a data, median is 5 and mode is 4, then mean is equal to :

While calculating mean of a grouped frequency distribution, step deviation method was used \(u = \frac{x-a}{h}\). It was found that \(\bar{x} = 64\), \(h = 5\) and \(a = 62.5\). The value of \(\bar{u}\) is

The mean of the following distribution is 53. Find the missing frequency p.

Hence, find mode of the distribution.}

Compute median of the following data :

The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :

Assertion (A) : The mean of first 'n' natural numbers is \( \frac{n - 1}{2} \).
Reason (R) : The sum of first 'n' natural numbers is \( \frac{n(n + 1)}{2} \).

An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. Find the modal age and median age of the policy holders.

If the mean and mode of a data are 12 and 21 respectively, then its median is :

The mean of the following frequency distribution is 35. Find the values of x and y, if the sum of frequencies is 25 :

If the mean and mode of a data are 12 and 21 respectively, then its median is :

The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data :

The upper limit of the median class of the above data is :

The mode of the following data is 3.286. Find the mean and median of the above data.

If dataset $A=\{1,2,3,\ldots,19\}$ and dataset $B=\{ax+b;\,x\in A\}$. If mean of $B$ is $30$ and variance of $B$ is $750$, then sum of possible values of $b$ is

Variates are given as \( -10, -7, -1, x, y, 2, 9, 16 \). If the mean \( (\mu) = \frac{7}{2} \) and variance = \( \frac{293}{4} \), find the mean of \( (1 + x + y), x, y, |y - x| \):

If the mean and variance of observations \( x, y, 12, 14, 4, 10, 2 \) is \(8\) and \(16\) respectively, where \( x>y \), then the value of \( 3x - y \) is: