Variance and Standard Deviation

IMPORTANT

Variance and Standard Deviation: Overview

This Topic covers sub-topics such as Standard Deviation, Variance, Variance and Standard Deviation, Coefficient of Variation in Statistics, Properties of Standard Deviation and, Properties of Variance

Important Questions on Variance and Standard Deviation

HARD

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 1

Find the mean, variance and standard deviation for the following frequency distribution:

Classes	$0 - 30$	$30 - 60$	$60 - 90$	$90 - 120$	$120 - 150$	$150 - 180$	$180 - 210$
Frequency	$2$	$3$	$5$	$10$	$3$	$5$	$2$

HARD

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 2

Find the mean, variance and standard deviation for the following frequency distribution:

Classes	$0 - 30$	$30 - 60$	$60 - 90$	$90 - 120$	$120 - 150$	$150 - 180$	$180 - 210$
Frequency	$2$	$3$	$5$	$10$	$3$	$5$	$2$

MEDIUM

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 3

The yield of sugar cane per acre for districts of a state is as under.

Districts	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$
Sugar cane	$12$	$10$	$15$	$19$	$21$	$16$	$18$	$9$	$25$	$10$

Calculate Standard deviation and coefficient of variation.

MEDIUM

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 4

The scores of a cricketer in $7$ matches are $70, 80, 60, 50, 40, 90, 95$ . Find the standard deviation.

HARD

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 5

Calculate Arithmetic Mean, Variance and Standard Deviation of the following data.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$3$	$7$	$12$	$15$	$8$	$3$	$2$

MEDIUM

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 6

The yield of sugar cane per acre for districts of a state is as under.

Districts	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$
Sugar cane	$12$	$10$	$15$	$19$	$21$	$16$	$18$	$9$	$25$	$10$

Calculate Standard deviation and coefficient of variation.

MEDIUM

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 7

Calculate the standard deviation and coefficient of standard deviation for the following data.

$X :$	$2$	$4$	$6$	$8$	$10$	$12$
$F :$	$5$	$15$	$20$	$25$	$25$	$20$

MEDIUM

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 8

If each of the observation $x_{1}, x_{2}, \dots, x_{n}$ is increased by ' $' a'$ ', where $a$ is a negative or positive number, show that the variance remains unchanged

HARD

IMPORTANT

mathematics>Statistics>Variance and Standard Deviation> Q 9

The mean of $5$ observations is $4.4$ and their variance is $8.24$ . If three of the observations are $1, 2$ and $6$ , find the other two observations.