The Insurance Institute for Highway Safety (www.iihs.org,...

The Insurance Institute for Highway Safety (www.iihs.org, June 11,2009 ) published data on repair costs for cars involved in different types of accidents. In one study, seven different 2009 models of mini- and micro-cars were driven at 6 mph straight into a fixed barrier. The following table gives the cost of repairing damage to the bumper for each of the seven models. $$ \begin{array}{lc} \text { Model } & \text { Repair Cost } \\ \hline \text { Smart Fortwo } & \$ 1,480 \\ \text { Chevrolet Aveo } & \$ 1,071 \\ \text { Mini Cooper } & \$ 2,291 \\ \text { Toyota Yaris } & \$ 1,688 \\ \text { Honda Fit } & \$ 1,124 \\ \text { Hyundai Accent } & \$ 3,476 \\ \text { Kia Rio } & \$ 3,701 \\ \hline \end{array} $$ Compute the values of the mean and median. Why are these values so different? Which of the two-mean or median-appears to be better as a description of a typical value for this data set?

The Insurance Institute for Highway Safety (www.iihs.org, June 11,2009 ) published data on repair costs for cars involved in different types of accidents. In one study, seven different 2009 models of mini- and micro-cars were driven at 6 mph straight into a fixed barrier. The following table gives the cost of repairing damage to the bumper for each of the seven models.
$$
\begin{array}{lc}
\text { Model } & \text { Repair Cost } \\
\hline \text { Smart Fortwo } & \$ 1,480 \\
\text { Chevrolet Aveo } & \$ 1,071 \\
\text { Mini Cooper } & \$ 2,291 \\
\text { Toyota Yaris } & \$ 1,688 \\
\text { Honda Fit } & \$ 1,124 \\
\text { Hyundai Accent } & \$ 3,476 \\
\text { Kia Rio } & \$ 3,701 \\
\hline
\end{array}
$$
Compute the values of the mean and median. Why are these values so different? Which of the two-mean or median-appears to be better as a description of a typical value for this data set?

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Key Concepts

Measures of Central Tendency

Measures of central tendency, such as the mean and median, summarize a typical value within a dataset. The choice between them depends on the distribution characteristics; the mean is useful when the data is symmetrically distributed, while the median is preferred when the data is skewed or contains outliers.

Outliers and Sensitivity

Outliers are extreme values that differ significantly from other observations. In datasets with outliers, the mean can be unduly influenced, which may not accurately reflect a typical or central value. The median, however, remains relatively unaffected by these outliers, providing a better representation of the central location in skewed distributions.

Mean

The mean is the arithmetic average obtained by summing all the data values and dividing by the number of values. It serves as a measure of central tendency, but it is highly sensitive to extreme values (outliers) that can sway the average significantly.

Median

The median is the middle value in a sorted list of data. It represents the center of a data set in such a way that half the values are smaller and half are larger, making it a robust measure of central tendency when the data includes outliers or is skewed.

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