Tag: measures of dispersion

Quizzes (8) Questions (118)

Questions Related to measures of dispersion

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

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?

  1. $-7$
  2. $-4$
  3. $7$
  4. $1.75$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=-2\times 3.5=-7$
Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

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

  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
Reveal answer Fill a bubble to check yourself
A,B Correct answer
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.

Multiple choice 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

Lowest value of variance can be:

  1. $1$
  2. $-1$
  3. $0$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $zero$
Multiple choice 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

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

  1. $2.4$
  2. $2.5$
  3. $2.7$
  4. $2.8$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

Multiple choice 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

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

  1. Mean Deviation

  2. Standard Deviation

  3. Quartile Deviation

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard deviation is defined mathematically as the square root of the variance, which is the mean of the squared deviations from the arithmetic mean.

Multiple choice 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

Which of the following are Methods of calculating Standard Deviation?

  1. Actual Mean Method

  2. Assumed Mean Method

  3. Step-Deviation Method

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Standard deviation can be calculated using the actual mean method, the assumed mean method, or the step-deviation method.

Multiple choice 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

Which of the following is true?

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Standard deviation is independent of the change of origin (adding or subtracting a constant from all values does not change the spread).

Multiple choice 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

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 ____.

  1. $4$
  2. $6$
  3. $3$

  4. None of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For any set of positive numbers, the relationship between Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) is GM^2 = AM * HM. Given AM=9 and GM=6, then 36 = 9 * HM, so HM = 4.