Tag: measures of dispersion and skewness

Quizzes (4) Questions (166)

Questions Related to measures of dispersion and skewness

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.

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

To find the median, it is necessary to arrange the data in _______.

  1. ascending order

  2. descending order

  3. ascending or descending order

  4. any of them
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the median, the data must be ordered by magnitude, which can be done in either ascending or descending order.

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

Calculate standard deviation of the following data.

X $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
f $10$ $8$ $15$ $8$ $4$
  1. $-12$
  2. $12$
  3. $12.36$
  4. $152.77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Marks Mid-values(X) f dxi$=X-25/10$ $fdx _if$ $dx _i^2$
$0-10$ $5$ $10$ $-2$ $-20$ $40$
$10-20$ $15$ $8$ $-1$ $-8$ $8$
$20-30$ $25$ $15$ $0$ $0$ $0$
$30-40$ $35$ $8$ $1$ $8$ $8$
$40-50$ $45$ $4$ $2$ $8$ $16$
Total $45$ $-12$ $72$

$\sqrt{\displaystyle\frac{72}{45}-\frac{144}{45\times 45}}\times 10$
$=12.36$