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

For a distribution, coefficient of variation is 22.5% and mean is 7.5 find the standard deviation___.

  1. 1.9975

  2. 1.6875

  3. 1.243

  4. 1.0943
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Coefficient of Variation (CV) = (SD / Mean) * 100. Given CV = 22.5% and Mean = 7.5, then 22.5 = (SD / 7.5) * 100. SD = (22.5 * 7.5) / 100 = 168.75 / 100 = 1.6875.

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

In a class of 100, the mean on a certain exam was 50, the standard deviation, 0. This means..........................

  1. half the class had scores less than 50

  2. there was a high correlation between ability and grade

  3. everyone had a score of exactly 50

  4. half the class had 0's and half had 50's
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. If standard deviation of a certain series is zero than it denotes that all the values of that series is equal to the mean of the series which made all the deviations zero and therefore standard deviation also 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

Average Marks of a group of $50$ students appeared in CA CPT exams is $134$ marks. If $10\%$ students scored more than $137$ marks, find the standard deviation of marks_____.

  1. $1.98$
  2. $2.336$
  3. $3.05$
  4. $2.98$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Assuming a normal distribution, 10% of students scored more than 137. This corresponds to the top 10% tail, where the z-score for 0.90 is approximately 1.28. Using the formula z = (x - mean) / SD, we get 1.28 = (137 - 134) / SD, so 1.28 = 3 / SD, SD = 3 / 1.28 = 2.34375. Option B is closest.

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 a population has a standard deviation of $2.25$, how large the sample should be to allow a maximum error of $0.33$ with $95\%$ confidence level?

  1. $252$
  2. $201$
  3. $220$
  4. $178$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The formula for sample size n is n = (z * sigma / E)^2. For a 95% confidence level, z = 1.96. Given sigma = 2.25 and E = 0.33, n = (1.96 * 2.25 / 0.33)^2 = (4.41 / 0.33)^2 = (13.3636)^2 = 178.58. Rounding up gives 179, but 178 is the closest option.

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

The standard deviation $\sigma$ of the first $N$ natural numbers can be obtained using which one of the following formula?

  1. $\sigma =\cfrac { { N }^{ 2 }-1 }{ 12 } $
  2. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 12 } } $
  3. $\sigma =\sqrt { \cfrac { N-1 }{ 12 } } $
  4. $\sigma =\sqrt { \cfrac { { N }^{ 2 }-1 }{ 6N } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\sigma^2=\dfrac{1}{n}\sum _{i=1}^{n}i^2-\left(\dfrac{1}{n}\sum _{i=1}^{n}i\right)^2$


     $=\dfrac{1}{n}(1^2+2^2+...+n^2)-\left(\dfrac{1}{n}(1+2+...+n)\right)^2$

     $=\dfrac{1}{n} \times \dfrac{n(n+1)(2n+1)}{6}-(\dfrac{n+1}{2})^2=\dfrac{n^2-1}{12}$

$\therefore \sigma=\sqrt{\dfrac{n^2-1}{12}}$

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

A researcher has collected the following sample data. The mean of the sample is 5.
3  5  12  3  2
The standard deviation is...............

  1. 8.944

  2. 4.062

  3. 13.2

  4. 16.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Data: 3, 5, 12, 3, 2. Mean = (3+5+12+3+2)/5 = 25/5 = 5. Variance = [(3-5)^2 + (5-5)^2 + (12-5)^2 + (3-5)^2 + (2-5)^2] / 5 = [4 + 0 + 49 + 4 + 9] / 5 = 66 / 5 = 13.2. SD = sqrt(13.2) = 3.63. If using sample SD (divide by n-1=4), Variance = 66/4 = 16.5, SD = sqrt(16.5) = 4.062.