What are common measures of central tendency (center) in statistics?
Answer
Three common measures of central tendency (center) used in statistics are mean, median, and mode.
The mean is the average value of the data. The sample mean \(\bar{y}\) is found by adding all of the values in the dataset together and then dividing by the number of observations. It is represented mathematically using the formula below. Each \(y_i\) represents a value in a dataset with n observations.
\[ \bar{y}=\frac{1}{n}\sum_{i=1}^{n}y_i \]
The median is the middle value in the data. It is also referred to as the 50th percentile because 50 percent of the data is less than the median. The sample median is found by ordering the data values from least to greatest and finding the middle value. If given the dataset {0, 3, 2, 4, 5, 1, 6}, the median value of 3 could be found by rewriting the data as 0, 1, 2, 3, 4, 5, 6.
Mode is the most frequent observation in the dataset. The mode is found by counting how many times each unique observation occurs in the dataset. Mode is used less in practice than mean and median, because it is possible to get more than one value for the mode.
