New York Stock Exchange (NYSE) Chairman Richard Grasso and...

New York Stock Exchange (NYSE) Chairman Richard Grasso and NYSE Board of Directors came under fire for the large compensation package being paid to Grasso. When it comes to salary plus bonus, Grasso's $\$ 8.5$ million out-earned the top executives of all major financial services companies. The data that follow show total annual salary plus bonus paid to the top executives of 14 financial services companies (The Wall Street Journal, September 17,2003 ). Data are in millions. a. What is the median annual salary plus bonus paid to the top executive of the 14 financial service companies? b. Provide a five-number summary. c. Should Grasso's $\$ 8.5$ million annual salary plus bonus be considered an outlier for this group of top executives? Explain. d. Show a box plot.

New York Stock Exchange (NYSE) Chairman Richard Grasso and NYSE Board of Directors came under fire for the large compensation package being paid to Grasso. When it comes to salary plus bonus, Grasso's $\$ 8.5$ million out-earned the top executives of all major financial services companies. The data that follow show total annual salary plus bonus paid to the top executives of 14 financial services companies (The Wall Street Journal, September 17,2003 ). Data are in millions.
a. What is the median annual salary plus bonus paid to the top executive of the 14 financial service companies?
b. Provide a five-number summary.
c. Should Grasso's $\$ 8.5$ million annual salary plus bonus be considered an outlier for this group of top executives? Explain.
d. Show a box plot.

Key Concepts

Median

The median is the middle value of an ordered dataset and serves as a measure of central tendency. It divides the dataset into two equal halves, meaning that 50% of the data points fall below it and 50% are above it. The median is often preferred over the mean in the presence of outliers because it is less influenced by extremely large or small values.

Five-Number Summary

The five-number summary is a set of descriptive statistics that provides a quick overview of a dataset's distribution. It includes the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. This summary helps identify the central tendency, spread, and potential asymmetry in the data, and it is commonly used in constructing box plots.

Outlier Detection

Outlier detection is the process of identifying data points that are significantly different from the rest of the dataset. A standard method involves using the interquartile range (IQR), which is the difference between Q3 and Q1. Data points that fall below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are typically considered outliers. Detecting outliers is important because they can influence statistical measures and may indicate unusual conditions or errors.

Box Plot

A box plot is a graphical display of a dataset's five-number summary. It shows the central 50% of the data as a box bounded by the first and third quartiles, with a line inside the box representing the median. 'Whiskers' extend from the box to the minimum and maximum values that are not considered outliers, and any outliers are often marked individually. This visualization helps in quickly assessing the distribution, variability, and potential outliers in the data.