# Coefficient of Skewness Karl Pearson developed a measure that describes the skewness of a…

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 23.

(e) Compute the coefficient of skewness for the data in Problem 24.

Problem 23

The Empirical Rule The following data represent the weights (in grams) of a random sample of 50 M&M plain candies.

(a) Determine the sample standard deviation weight. Express your answer rounded to three decimal places.

(b) On the basis of the histogram drawn in Section 3.1, Problem 25, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of M&Ms.

(c) Use the Empirical Rule to determine the percentage of M&Ms with weights between 0.803 and 0.947 gram. .

(d) Determine the actual percentage of M&Ms that weigh between 0.803 and 0.947 gram, inclusive.

(e) Use the Empirical Rule to determine the percentage of M&Ms with weights more than 0.911 gram.

(f) Determine the actual percentage of M&Ms that weigh more than 0.911 gram

Problem 25

Which Car Would You Buy? Suppose that you are in the market to purchase a car. You have narrowed it down to two choices and will let gas mileage be the deciding factor. You decide to conduct a little experiment in which you put 10 gallons of gas in the car and drive it on a closed track until it runs out gas. You conduct this experiment 15 times on each car and record the number of miles driven.

Describe each data set. That is, determine the shape, center, and spread. Which car would you buy and why?

Problem 24

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.

(a) Determine the sample standard deviation length of eruption. Express your answer rounded to the nearest whole number.

(b) On the basis of the histogram drawn in Section 3.1, Problem 26, comment on the appropriateness of using the Empirical Rule to make any general statements about the length of eruptions.

(c) Use the Empirical Rule to determine the percentage of eruptions that last between 92 and 116 seconds.

(d) Determine the actual percentage of eruptions that last between 92 and 116 seconds, inclusive.

(e) Use the Empirical Rule to determine the percentage of eruptions that last less than 98 seconds.

(f) Determine the actual percentage of eruptions that last less than 98 seconds

Problem 26

Which Investment Is Better? You have received a year-end bonus of $5000. You decide to invest the money in the stock market and have narrowed your investment options down to two mutual funds. The following data represent the historical quarterly rates of return of each mutual fund for the past 20 quarters (5 years).

Describe each data set. That is, determine the shape, center, and spread. Which mutual fund would you invest in and why?