Forbes magazine prints an annual Top-Earning Nonliving...

Forbes magazine prints an annual Top-Earning Nonliving Celebrities list (based on royalties and estate earnings). Find the mean, median, mode, and midrange for the data. Comment on the skewness. Figures represent millions of dollars. $\begin{array}{lll}{\text { Kurt Cobain }} & {50} & {\text { Ray Charles }} & {10} \\ {\text { Elvis Presley }} & {42} & {\text { Marilyn Monroe }} & {8} \\ {\text { Charles } \mathrm{M} . \text { Schulz }} & {35} & {\text { Johnny Cash }} & {8} \\ {\text { John Lennon }} & {24} & {\text { Johnny Cash }} & {8} \\ {\text { Albert Einstein }} & {20} & {\text { George Harrison }} & {7} \\ {\text { Andy Warhol }} & {19} & {\text { Bob Marley }} & {7} \\ {\text { Theodore Geisel }} & {10} & {} \\ {\text { (Dr. Seuss) }}\end{array}$

Forbes magazine prints an annual Top-Earning Nonliving Celebrities list (based on royalties and estate earnings). Find the mean, median, mode, and midrange for the data. Comment on the skewness. Figures represent millions of dollars.
$\begin{array}{lll}{\text { Kurt Cobain }} & {50} & {\text { Ray Charles }} & {10} \\ {\text { Elvis Presley }} & {42} & {\text { Marilyn Monroe }} & {8} \\ {\text { Charles } \mathrm{M} . \text { Schulz }} & {35} & {\text { Johnny Cash }} & {8} \\ {\text { John Lennon }} & {24} & {\text { Johnny Cash }} & {8} \\ {\text { Albert Einstein }} & {20} & {\text { George Harrison }} & {7} \\ {\text { Andy Warhol }} & {19} & {\text { Bob Marley }} & {7} \\ {\text { Theodore Geisel }} & {10} & {} \\ {\text { (Dr. Seuss) }}\end{array}$

Key Concepts

Skewness

Skewness describes the asymmetry in the distribution of a data set. A distribution can be right-skewed (positively skewed) if the tail on the right side is longer, or left-skewed (negatively skewed) if the tail on the left side is longer. Understanding skewness is important as it affects which measure of central tendency (mean, median, or mode) is most representative for the data.

Mode

The mode is the most frequently occurring value in a data set. It helps identify the common trend or category in the data, and in cases where multiple values appear with the same frequency, the data set can be multimodal.

Midrange

The midrange is the average of the smallest and largest values in a data set. While it provides a simple measure of central tendency, it is highly sensitive to extreme values, which can make it less reliable if the data includes significant outliers.

Mean

The mean is the arithmetic average of a data set, calculated by summing all the values and dividing by the number of observations. It serves as a measure of central tendency but can be sensitive to extreme values or outliers, which can distort its representation of the data’s center.

Median

The median is the middle value of an ordered data set that divides it into two equal halves. As a measure of central tendency, it is more robust in the presence of outliers or skewed data since it is not influenced by extremely high or low values.

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