Statistics — Class 12 Mathematics PYQs

The mean of $n$ observations $1,4,9,16,\dots ,n^2$ is $130$. What is the value of $n$?

Let $x+2y+1=0$ and $2x+3y+4=0$ are two lines of regression computed from some bivariate data. If $\theta$ is the acute angle between them, then what is the value of $488\tan 3\theta$?

An edible oil is sold at the rates $150,200,250,300$ rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year during these years, what is the average price of oil in rupees (approximately) per litre?

Consider the following for the next two (02) items that follow:

$x_i$	$1$	$2$	$3$	$\dots$	$n$
$f_i$	$1$	$2^{-1}$	$2^{-2}$	$\dots$	$2^{-(n-1)}$

What is the mean of the distribution?

Consider the following for the next two (02) items that follow:

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41.

What is the mean deviation of the largest five observations?

Consider the following for the next two (02) items that follow:

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41.

What is the variance of the largest five observations?

The mean and variance of five observations are $14$ and $13\cdot 2$ respectively. Three of the five observations are $11,16$ and $20$. What are the other two observations?

The sum of deviations of $n$ numbers from $10$ and $20$ are $p$ and $q$ respectively. If $(p-q{)}^2=10000$, then what is the value of $n$ ?

If $\bar{X}=20$ is the mean of $10$ observations $x_1,x_2,\dots ,x_{10}$; then what is the value of
${\sum }_{i=1}^{10}\left(\frac{3x_i-4}{5}\right)$ ?

If the mean and the sum of squares of $10$ observations are $40$ and $16160$ respectively, then what is the standard deviation ?