Variance and Standard Deviation

IMPORTANT

Variance and Standard Deviation: Overview

This topic covers concepts, such as, Variance and Standard Deviation, Variance, Merits & Demerits of Standard Deviation as Measures of Dispersion etc.

Important Questions on Variance and Standard Deviation

MEDIUM

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 1

Find the standard deviation using the short-cut method.

Height [cms]	Number of Children
$70 - 75$	$3$
$75 - 80$	$4$
$80 - 85$	$7$
$85 - 90$	$7$
$90 - 95$	$15$
$95 - 100$	$9$
$100 - 105$	$6$
$105 - 110$	$6$
$110 - 115$	$3$

MEDIUM

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 2

Find the variance using the short-cut method.

Height [cms]	Number of Children
$70 - 75$	$3$
$75 - 80$	$4$
$80 - 85$	$7$
$85 - 90$	$7$
$90 - 95$	$15$
$95 - 100$	$9$
$100 - 105$	$6$
$105 - 110$	$6$
$110 - 115$	$3$

MEDIUM

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 3

For $2 n$ observations $a_{1}, - a_{1}, a_{2}, - a_{2}, a_{3}, - a_{3}, ........., a_{n}, - a_{n}$ where all $a$ 's are distinct. Let $\bar{x}$ , $σ$ and $M$ denotes mean, standard deviation and median, respectively. Then which of the following option is incorrect when $n$ is an odd integer?

MEDIUM

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 4

The following gives the number of books taken in a school library in $7$ days. Find the variance(up to two decimals) of the books taken.

$7, 9, 12, 15, 5, 4, 11$

MEDIUM

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 5

Find the $S . D .$ for the number of days patients admitted in a hospital(up to two decimals).

Days of confinement	$5$	$6$	$7$	$8$	$9$
No. of patients	$18$	$14$	$9$	$3$	$1$

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Mathematics>Statistics>Variance and Standard Deviation> Q 6

If the coefficient of variation is $50 %$ and standard deviation is $4$ , then find mean.

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Mathematics>Statistics>Variance and Standard Deviation> Q 7

The expression of standard deviation as a percentage of the mean is the coefficient of variation.

MEDIUM

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Mathematics>Statistics>Variance and Standard Deviation> Q 8

The mean and standard deviation from $18$ observations are $14$ and $12$ . If additional observation $8$ is to be included, find corrected mean and variance.

HARD

IMPORTANT

Mathematics>Statistics>Variance and Standard Deviation> Q 9

Find the standard deviation for the distribution given below:

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Frequency	$10$	$20$	$30$	$35$	$14$	$10$	$2$

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Mathematics>Statistics>Variance and Standard Deviation> Q 10

A retailer uses two different formulas for predicting monthly sales. The first formula has an average of $700$ records, and a standard deviation of $35$ records. The second formula has an average of $300$ records, and a standard deviation of $16$ records. What is the ratio of coefficient of variation of first formula to that of second formula?(upto two decimals).

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Mathematics>Statistics>Variance and Standard Deviation> Q 11

The square root of variance of a distribution is known as

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Mathematics>Statistics>Variance and Standard Deviation> Q 12

Find the variance of the set $\{x \in ℕ : 0 < x < 2\}$ .

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Mathematics>Statistics>Variance and Standard Deviation> Q 13

Find the variance of the set $\{2 x, 4 x, 6 x\}$ .