Data Analysis and Statistics・Visualization

Collected data is nothing more than a list of numbers on its own. It becomes meaningful only after being summarized with statistics and visualized in graphs. In this lesson, you will learn the basics of statistics—measures of central tendency, variation, and correlation—as well as points to keep in mind when interpreting data correctly.

Measures of Central Tendency — Summarizing Data with One Number

A value that represents the characteristics of an entire data set with one number is called a measure of central tendency.

・Mean: The sum of all values divided by the number of data points.
・Median: The middle value when the data is arranged from smallest to largest.
・Mode: The value that appears most often.

Measures of Variation — Variance and Standard Deviation

Even when the mean is the same, the way data is spread out may differ. Variance and standard deviation show the amount of variation. Variance is “the average of the squared differences (deviations) between each data value and the mean,” and standard deviation is the positive square root of the variance. The larger the standard deviation, the more widely the data is spread out. For example, for the data 2、4、6、8、10 (mean 6), the deviations are −4、−2、0、2、4, and the average of their squares is (16＋4＋0＋4＋16)÷5 ＝ 8. The variance is 8, and the standard deviation is √8 ≒ 2.83.

Correlation — Examining the Relationship between Two Quantities

To examine the relationship between two quantities, such as “ice cream sells more on hotter days,” use a scatter plot, which places the two quantities on the horizontal and vertical axes and plots points. When one quantity tends to increase as the other increases, this is called a positive correlation; when one tends to decrease as the other increases, it is called a negative correlation. The strength of the relationship is represented by the correlation coefficient (a value from −1 to 1), where a value closer to 1 means a strong positive correlation, a value closer to −1 means a strong negative correlation, and a value closer to 0 means a weak correlation.

Correlation and Causation Are Different

The most important point to keep in mind in data analysis is that correlation does not necessarily mean causation. For example, there is a positive correlation between “ice cream sales” and “the number of drowning accidents,” but ice cream does not cause the accidents. The third factor of “temperature” behind them increases both. This kind of apparent correlation is called a spurious correlation. When you find a correlation, always question whether “it could be due to chance,” “there could be a hidden factor,” or “the direction of causation could be reversed.”

Choose a Graph That Matches the Purpose

For visualization, choose a graph according to what you want to communicate. Bar graphs are suitable for comparing quantities, line graphs for changes over time, pie charts for proportions of a whole, scatter plots for relationships between two quantities, and histograms for data distributions. Because a graph that omits part of the vertical axis can make differences appear larger than they really are, you must also be careful when “reading” graphs.

Practice Problems

1. Find the mean and median of the data 4、6、8、10、12.
2. For income data that includes a very small number of high-income earners, which is more appropriate as a “measure of central tendency close to the actual situation,” the mean or the median? Answer with a reason.
3. When a correlation is found that “students who eat breakfast tend to have higher grades,” explain why you cannot immediately conclude that “breakfast raises grades.”