Measures of central tendency
Find suitable summary values and compare their meanings and limitations.
Meaning
The mean, median, and mode summarize data in different ways. The mean is the sum divided by the count. The median is the middle of the sorted data, or the average of the two middle values for an even count. The mode is the most frequent value.
Example
For 1, 2, 2, 3, and 17, the mean is 5, the median is 2, and the mode is also 2. The large value 17 pulls the mean above most values. The sum is 1+2+2+3+17=25; sharing it equally among five values gives 5. Five copies of the mean preserve the original total 25. The median instead selects the middle position in sorted order, answering a different question. One summary value cannot describe the entire distribution. Sort before finding the median, and use appropriate weights when combining means from groups of different sizes.
Practice for this concept
Scope and references
Topics
Mean, median, mode, weighted mean
Learning goal
Find suitable summary values and compare their meanings and limitations.
Helpful background
Check the number and sum of values and the division needed for the summary.
Mean, median, and mode
Does not cover weighted means or every situation for choosing a summary value.