Describing Data Numerically: The Four Measures

There are four groups of measures that can be used in describing data. Click the provided links to review the measures of:

1. the center (central location)
• mode
• median
• mean



Click here to view the difference between median and mean




2. spread (variability)
• range
• variance
• standard deviation
• less often used measures: interquartile range and mean absolute deviation



3. asymmetry (skewness)



view an interactive illustration of this concept the relationship of the measures of central tendency in symmetric and in skewed distributions




4. flatness/peakedness (kurtosis)

Among the four measures, research reports in education and the social sciences rarely mention measure of kurtosis.

You must have read that median, one of the three most often used measures of central location, is also known as 50th percentile (%ile).

Also, one measure of variability is computed by getting the distance between the first and third quartiles. Quartile is a special name for some specific percentiles.

Many standardized test scores are expressed in %iles. Click here to review this topic.

Another commonly reported score in standardized tests is the z-score. Click here to learn more about this topic.

Links you might be useful when you're already a teacher using a spreadsheet for your class records: Calculating for mean, median and mode using MS-Excel Using MS-Excel's basic statistical functions