There are three ways to measure the center of a dataset, to summarize a whole column of quantitative data using just one number:

  • The mean of a dataset is the average of all the numbers.

  • The median of a dataset is a value that is smaller than half the dataset, and larger than the other half. In an ordered list the median will either be the middle number or the average of the two middle numbers.

  • The mode(s) of a dataset is the value (or values) occurring most often. When all of the values occur equally often, a dataset has no mode.

In a symmetric dataset, values are just as likely to occur a certain distance above the mean as below the mean, and the median and mean are usually close together.

When a dataset is asymmetric, the median is a more decriptive measure of center than the median.

  • A dataset with left skew has a few values that are unusually low, which pull the mean below the median.

  • A dataset with right skew has a few values that are unusually high, which pull the mean above the median.

When a dataset contains a small number of values, the mode may be the most descriptive measure of center.

Data Scientists can also measure the spread of a dataset using a five-number summary:

  • The minimum – the lowest value in the dataset

  • The first, or “lower” quartile (Q1) – the middle of the lower half of values, which separates the lowest quarter from the next smallest quarter

  • The second quartile (Q2) – the middle value, which separates the entire dataset into “top” and “bottom” halves

  • The third, or “upper” quartile (Q3) – the middle of the higher half of values which separates the second highest quarter from the highest quarter

  • The maximum – the largest value in the dataset

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