Bissoy.com
Doctors Medicines MCQs Q&A

The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness βz ?

The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness βz ? Correct Answer 1.125

Given

μ2 = 4

μ4 = 18

Formula used

Karl pearson's coefficient of skewness βz = μ4/μ22

Calculaton

Karl Pearson defined the following four coefficients, based upon the first four moments"about mean:

⇒ βz = 18/42

⇒ βz = 18/16

∴ The value of Pearson's coefficient of skewness βz is 1.125

Important Points

Moment = The rth moment of a variable x about any point x = A, usually denotted by μr' and it is given by

μr' = (1/N)[∑fi(xi - A)r , ∑fi = N

⇒  (1/N)[∑fidir  di = (xi - A)

Moment about mean = The rth moments of a variable about the mean x̅  denoted by μ =(1/N)[∑fi(xi - x̅ )r = (1/N)[∑fizir  where zi = xi - x̅

 

 

Related Questions

Which two of the following statements are true?  a) Skewness studies the flatness or peakedness of the distribution  b) A positively skewed distribution curve is stretched more to the right than to the left  c) On the basis of empirical relationship between mean, mode and median for moderately asymmetrical distribution, Karl Pearson's coefficient of skewness can be measured by 3 (Mean -Median) divided by Standard Deviation  d) If mean < mode, the distribution is positively skewed  Choose the correct option from those below: 
Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. In the last four years, a man donated 5%, 8%, 10% and 12% of his income respectively. He had also received an increment of 15%, 20% and 25% in the second, third and fourth year respectively. Quantity A: What is the percentage increase in his donation in second year as compared to the first year? Quantity B: What is the percentage increase in his donation in third year as compared to the second year? Quantity C: What is the percentage increase in his donation in fourth year as compared to the third year?
Shikha went to the market to purchase five fans. The cost of the first fan is 25% more than the second fan and price of third fan is 20% less than fourth fan and price of fifth fan is 16% more than price of fourth fan. Price of the fourth fan is 3/4th of the second fan’s price. If the average cost of the first three fans was Rs.35 more than of the last three fans. What is  the cost of the second costliest fan?
Which of the following statements are true? a. The correlation coefficient is dependent on the choice of both origin and scale observations. b. The correlation coefficient is dependent on the units of measurements. c. The coefficient of correlation is the square root of the coefficient of determination. d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable.
Approximately, the coefficient of variation for the given data where Pearson's second measure of skewness = 0.42, arithmetic mean = 86 and median = 80, is: 
Statement I Exponential probability distribution has the mean = $$\frac{1}{\mu }$$ and variance = $$\frac{1}{{{\mu ^2}}}$$
Statement II The mean, median and mode do not coincide in the normal distribution.
Statement III The binomial distribution is symmetrical for any value of p (probability of success).
If moment coefficient about aerodynamic centre of wing is -0.216 and lift coefficient of wing is 1.2. Find moment coefficient about cg. Given cg location as Xcg = 0.3.
A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twenty-fourth of its capacity, during the second hour at one-twelfth of its capacity, during the third hour at one-eighth of its usual capacity, during the fourth hours at one-fourth of its usual capacity and during the fifth hour it was only one-half as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank a constant rate, the empty cistern could be filled in 5 hours, all the three pipe working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?
When coefficient of skewness is zero the distribution is
When coefficient of skewness is zero, the distribution is