List of top Mathematics Questions on Statistics

Mode of data 2, 3, 3, 5, 7 is ____.

The mean of number 2, 4, 6, 8 is ____.

If all observations are increased by 5 their mean ____.

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

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

The average age of 100 teachers in a college in 2000 was 50 years. In 2002, 20 teachers superannuated from their jobs, whose average age was 60 years. In 2005, 40 new teachers joined the college whose average age was 38 years. What was the average age of all the teachers in 2008?

The mean and standard deviation of 100 items are 50 and 4, respectively then the sum of all squares of the items is

If the mean and standard deviation of 10 observations are 24 and 4 respectively, then the sum of the squares of all observations is

The combined mean age of a group of boys and girls in a school is 12. If the mean of the boys in that group is 14 and the mean of the girls is 9, then the percentage of boys in that group is

Find mean and mode of the following frequency distribution :

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

For 10 observations \(x_1, x_2, \dots, x_{10}\), if \(\sum_{i=1}^{10} (x_i + 2)^2 = 180\) and \(\sum_{i=1}^{10} (x_i - 1)^2 = 90\), then their standard deviation is:

Suppose that the mean and median of the non-negative numbers 21, 8, 17, \(a\), 51, 103, \(b\), 13, 67, \((a>b)\), are 40 and 21, respectively. If the mean deviation about the median is 26, then \(2a\) is equal to:

A data consists of 20 observations $x_1, x_2, \dots, x_{20}$. If $\sum_{i=1}^{20} (x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20} (x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:

If \( \sum_{i=1}^{10} (x_i + 2)^2 = 180 \) and \( \sumᵢ=1¹0 (xᵢ - 1)² = 90 , then the Standard Deviation is equal to

Consider the differential equation \[ \sin\left(\frac{y}{x}\right)\frac{dy}{dx} + 1 = \frac{y}{x}\sin\left(\frac{y}{x}\right) \] with \( y(1) = \frac{\pi}{2} \). Let \[ \alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right). \] If \( r \) is the radius of the circle \[ x^2 + y^2 - 2px + 2py + \alpha + 2 = 0, \] then the number of integral values of \( p \) is:

A and B play a tennis match which will not result in a draw. The player who wins 5 rounds first will be the winner of the match. The number of ways such that A can win the match is:

If \( x_1, x_2, \dots, x_{25} \) be 25 observations such that \( \sum_{i=1}^{25} (x_i + 5)^2 = 2500 \) and \( \sum_{i=1}^{25} (x_i - 5)^2 = 1000 \). Then, the ratio of Mean and Standard deviation of the given observations is:

Let mean and median of 9 observations 8, 13, a, 17, 21, 51, 103, b, 67 are 40 and 21 respectively where a > b. If mean deviation about median is 26 then 2a is :-

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

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 :

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:

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.