The following list shows the 15 largest banks in the world...

The following list shows the 15 largest banks in the world by assets according to Standard and Poor's. Compute the median and the mean assets from this group. Which of these two measures do you think is most appropriate for summarizing these data and why? What is the value of $Q_{2}$ and of $Q_{3}$ ? Determine the 63 rd percentile for the data. Determine the 29th percentile for the data. How could such information on percentiles potentially help banking decision makers? $$ \begin{array}{|l|c|} \hline \text { Bank } & \text { Assets (\$ billions) } \\ \hline \text { Industrial \& Commercial Bank of China (ICBC) } & 4009 \\ \hline \text { China Construction Bank Corp. } & 3400 \\ \hline \text { Agricultural Bank of China } & 3236 \\ \hline \text { Bank of China } & 2992 \\ \hline \text { Mitsubishi UFJ Financial Group } & 2785 \\ \hline \text { JPMorgan Chase \& Co. } & 2534 \\ \hline \text { HSBC Holdings } & 2522 \\ \hline \text { BNP Paribas } & 2357 \\ \hline \text { Bank of America } & 2281 \\ \hline \text { Credit Agricole } & 2117 \\ \hline \text { Wells Fargo \& Co. } & 195^{2} \\ \hline \text { Japan Post Bank } & 1874 \\ \hline \text { Citigroup Inc. } & 1842 \\ \hline \text { Sumitomo Mitsui Financial Group } & 1775 \\ \hline \text { Deutsche Bank } & 1766 \\ \hline \end{array} $$

The following list shows the 15 largest banks in the world by assets according to Standard and Poor's. Compute the median and the mean assets from this group. Which of these two measures do you think is most appropriate for summarizing these data and why? What is the value of $Q_{2}$ and of $Q_{3}$ ? Determine the 63 rd percentile for the data. Determine the 29th percentile for the data. How could such information on percentiles potentially help banking decision makers?
$$
\begin{array}{|l|c|}
\hline \text { Bank } & \text { Assets (\$ billions) } \\
\hline \text { Industrial \& Commercial Bank of China (ICBC) } & 4009 \\
\hline \text { China Construction Bank Corp. } & 3400 \\
\hline \text { Agricultural Bank of China } & 3236 \\
\hline \text { Bank of China } & 2992 \\
\hline \text { Mitsubishi UFJ Financial Group } & 2785 \\
\hline \text { JPMorgan Chase \& Co. } & 2534 \\
\hline \text { HSBC Holdings } & 2522 \\
\hline \text { BNP Paribas } & 2357 \\
\hline \text { Bank of America } & 2281 \\
\hline \text { Credit Agricole } & 2117 \\
\hline \text { Wells Fargo \& Co. } & 195^{2} \\
\hline \text { Japan Post Bank } & 1874 \\
\hline \text { Citigroup Inc. } & 1842 \\
\hline \text { Sumitomo Mitsui Financial Group } & 1775 \\
\hline \text { Deutsche Bank } & 1766 \\
\hline
\end{array}
$$

Key Concepts

Data Distribution Summary

When choosing the most appropriate summary statistic, it is essential to consider the shape and distribution of the data. In cases where the data may be skewed or contain outliers, the median offers a reliable central tendency measure over the mean. Additionally, percentiles and quartiles provide detailed insights into the dispersion and spread of the data, facilitating comparisons and decision-making processes in settings such as financial assessment and risk evaluation.

Percentiles and Quartiles

Percentiles are values that divide a data set into 100 equal parts, indicating the relative standing of a value within the distribution. Quartiles are specific percentiles (the 25th, 50th, and 75th) that split the data into four equal segments. The median is the 50th percentile (or second quartile, Q2), and the third quartile (Q3) is the 75th percentile. These measures help in understanding the spread and concentration of data, which is valuable for making decisions based on the distribution of values.

Mean

The mean is a measure of central tendency calculated by summing all the data values and dividing by the number of observations. It is useful for providing an overall average but can be heavily influenced by extreme values or outliers, which may distort its representation of the central location for a skewed distribution.

Median

The median is the middle value in a data set when it is arranged in numerical order. This measure is robust to outliers and skewed data, making it particularly useful in summarizing data that contain extreme values, as it provides a more accurate reflection of a typical value in the distribution.

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