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Solved: Coefficient of Skewness Karl Pearson developed a
Chapter 9, Problem 43AYU(choose chapter or problem)
Coefficient of Skewness Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is
The value of this measure generally lies between −3 and +3. The closer the value lies to −3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right. A value close to 0 indicates a symmetric distribution. Find the coefficient of skewness of the following distributions and comment on the skewness.
(a) Mean = 50, median = 40, standard deviation = 10
(b) Mean = 100, median = 100, standard deviation = 15
(c) Mean = 400, median = 500, standard deviation = 120
(d) Compute the coefficient of skewness for the data in Problem 1.
(e) Compute the coefficient of skewness for the data in Problem 2.
Problem 1
The Empirical Rule The following data represent the weights (in grams) of a random sample of 50 M&M plain candies.
Problem 2
The Empirical Rule The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geyser in Calistoga, California.
Questions & Answers
QUESTION:
Coefficient of Skewness Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is
The value of this measure generally lies between −3 and +3. The closer the value lies to −3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right. A value close to 0 indicates a symmetric distribution. Find the coefficient of skewness of the following distributions and comment on the skewness.
(a) Mean = 50, median = 40, standard deviation = 10
(b) Mean = 100, median = 100, standard deviation = 15
(c) Mean = 400, median = 500, standard deviation = 120
(d) Compute the coefficient of skewness for the data in Problem 1.
(e) Compute the coefficient of skewness for the data in Problem 2.
Problem 1
The Empirical Rule The following data represent the weights (in grams) of a random sample of 50 M&M plain candies.
Problem 2
The Empirical Rule The following data represent the length of eruption for a random sample of eruptions at the Old Faithful geyser in Calistoga, California.
ANSWER:
Step 1 of 5
(a)
The coefficient of skewness formula is,
Given,
Mean = 50,
Median = 40,
Standard deviation = 10
Substituting the values into the formula, we get
It’s also given that the value of this measure generally lies between -3 and +3. The closer the value lies to -3, the more the distribution is skewed left. The closer the value lies to +3, the more the distribution is skewed right.
Here we got the coefficient of skewness as +3 using the formula. Therefore, the given distribution is right skewed.