3.1: 什么是中心趋势？

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large quantities of data and developing an inference, one needs to identify a value representative of the entire data set. Characteristics such as central tendency, extreme values, range of measurements, or the most repeated value can help better understand the data.

The central tendency is the most conventionally used data characteristic. It is a statistical measure identifying a single value uniquely representative of the data.

The mean, median, mode, and midrange are the four essential measures of central tendency and have advantages and disadvantages over each other.

Mean: The mean is defined as the average value of a data set. However, a critical disadvantage of the mean is that it is sensitive to extreme values, called outliers, especially if the sample size is small.

Median: The median is the central or middle value in a data set when all data elements are arranged in an increasing or decreasing order. The median is generally a better measure of the center when there are extreme values or outliers because it is not affected by the precise numerical values of the outliers.

Mode: The mode is defined as the most frequent value of a data set. Bimodal data has two modes, and multimodal data has more than two modes. Mode is the only measure of center for the nominal level of measurement.

Midrange: The midrange provides the midpoint between two extreme values in a data set. Although it is easy to compute, it is susceptible to outliers and rarely used in statistics.