Statistics — NDA Mathematics PYQs

*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?

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 statements is correct?

The arithmetic mean of $100$ observations is $50$. If $5$ is subtracted from each observation and then divided by $20$, then what is the new arithmetic mean?

The standard deviation of $100$ observations is $10$. If $5$ is added to each observation and then divided by $20$, then what will be the new standard deviation?

What is the arithmetic mean of $8^2,9^2,10^2,\dots ,15^2$?

What is the harmonic mean of the numbers $\left(\genfrac{}{}{0ex}{}{10}{3}\right)$, $\left(\genfrac{}{}{0ex}{}{10}{4}\right)$, $\left(\genfrac{}{}{0ex}{}{10}{5}\right)$, $\left(\genfrac{}{}{0ex}{}{10}{6}\right)$ and $\left(\genfrac{}{}{0ex}{}{10}{7}\right)$?