Tag: measures of dispersion

Questions Related to measures of dispersion

If the standard deviation of $x _1, x _2, .., x _n$ is $3.5$, then the standard deviation of $-2x _1-3, -2x _2-3$,....., -2x_n-3$ is?

maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

  1. $-7$

  2. $-4$

  3. $7$

  4. $1.75$

Show answer
Correct Option: A
Explanation:
The Standard Deviation of a set remains unchanged if each data is increased or decreased by a constant however changes similarly when data is multiplied or divided by a constant.
$\therefore $ The SD for the new data set will be $=-2\times 3.5=-7$

Consider the following statements.Which of these is/are correct?

maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

  1. Mode can be computed from histogram

  2. Median is not independent of change of scale

  3. Variance is independent of change of origin and scale

  4. none of these

Show answer
Correct Option: A,B
Explanation:

If we change scale by using x + h then median increases by h.
so median is not independent of change of scale.
From histogram we can see highest frequency so made.
Hence, options 'A' and 'B' are correct.

Standard deviation is calculated from the Harmonic Mean (HM).

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Always

  2. Sometimes

  3. Never

  4. None of these

Show answer
Correct Option: C
Explanation:

Standard deviation is calculated from mean $i.e$ arithmetic mean.

It never be calculated from harmonic mean.

Lowest value of variance can be:

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $1$

  2. $-1$

  3. $0$

  4. None of these

Show answer
Correct Option: C
Explanation:
We know that $Var(x)=E(X^2)-(E(x))^2$

Variance is non-negative because the squares are positive or zero.

Therefore, $Var(X)\geq 0$

Hence, the lowest value of variance is $zero$

What is the standard deviation of $7,9,11,13,15$?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $2.4$

  2. $2.5$

  3. $2.7$

  4. $2.8$

Show answer
Correct Option: A
Explanation:

Given numbers are $ 7,9,11,13,15$
Mean of given numbers $=\dfrac { 7+9+11+13+15 }{ 5 } =11$
Standard deviation$=\dfrac { |7-11|+|9-11|+|11-11|+|13-11|+|15-11| }{ 5 } =2.4$
Option A is true

__________ is the positive square root of the mean of squared deviations from mean. 

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Mean Deviation

  2. Standard Deviation

  3. Quartile Deviation

  4. None of the above

Show answer
Correct Option: B

Which of the following are Methods of calculating Standard Deviation?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Actual Mean Method

  2. Assumed Mean Method

  3. Step-Deviation Method

  4. All of these

Show answer
Correct Option: D

Which of the following is true?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. Standard Deviation is not affected by the value of the constant from which deviations are calculated.

  2. The value of the constant does not figure in the standard deviation formula

  3. Standard Deviation is Independent of Origin.

  4. All of these

Show answer
Correct Option: D

Which of the following represents median?

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. First quartile

  2. Fiftieth percentile

  3. Sixth decile

  4. None of the above

Show answer
Correct Option: B

If the A.M of a set of observations is $9$ and its G.M is $6$. Then the H.M of the set of observations is ____.

business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

  1. $4$

  2. $6$

  3. $3$

  4. None of them

Show answer
Correct Option: A