Statistics — NDA Mathematics PYQs

Let two lines of regression be $x+y+11=0$ and $2x+3y+4=0$ for some data. What is the value of correlation coefficient between $x$ and $y$ ?

If the mean of 20 observations, namely $x_1,x_2,x_3,\dots ,x_{20}$ is $1\cdot 414$, then what is the value of ${\sum }_{i=1}^{20}100(2x_i+4)$ ?

The standard deviation of 100 observations is 10. If 5 is multiplied to each of the observations, then what is the new standard deviation ?

*Directions : For the next two (02) items that follow :

The frequency distribution of marks obtained by 100 students in a certain subject is given below :

$$\begin{array}{lcccc}\text{Marks}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40\\ \text{No. of students}& 10& 20& f& 40\end{array}$$*

What is the mean deviation about the arithmetic mean ?

*Directions : For the next two (02) items that follow :

The frequency distribution of marks obtained by 100 students in a certain subject is given below :

$$\begin{array}{lcccc}\text{Marks}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40\\ \text{No. of students}& 10& 20& f& 40\end{array}$$*

What is the standard deviation ?

*Consider the following for the four (04) items that follow :
The frequency distribution of height of students of a class is given below :

Height (in cm)	Number of Students
160-162	12
162-164	15
164-166	24
166-168	13

What is the total number of students whose height is less than or equal to $165$ cm?

*Consider the following for the four (04) items that follow :
The frequency distribution of height of students of a class is given below :

Height (in cm)	Number of Students
160-162	12
162-164	15
164-166	24
166-168	13

What is the median height of the class?

*Consider the following for the four (04) items that follow :
The frequency distribution of height of students of a class is given below :

Height (in cm)	Number of Students
160-162	12
162-164	15
164-166	24
166-168	13

The height which occurs most frequently in the class is

*Consider the following for the four (04) items that follow :
The frequency distribution of height of students of a class is given below :

Height (in cm)	Number of Students
160-162	12
162-164	15
164-166	24
166-168	13

The most appropriate graphical representation of the given frequency distribution is

Consider the following for the two (02) items that follow :
The sum and the sum of squares of the observations corresponding to length $X$ (in cm) and weight $Y$ (in gm) of $50$ tropical tubers are given as $\sum X=200$, $\sum Y=250$, $\sum X^2=900$ and $\sum Y^2=1400$.

Which one of the following is correct?