Find Median

The median value it’s a value that’s similar in interpretation to the arithmetic mean, but that doesn’t get thrown off by a single crazy-big or small data point. So how is the median value actually calculated? It’s remarkably easy. The first step is to write the data in our sample in order from smallest to largest. Now, the median value is simply defined to be the number in the middle.

That ability to resist outliers is exactly why the median value is such a useful and important statistic for describing many measurable quantities in the real-world—for example: average housing prices. Why? Well, most cities tend to have lots of mid-priced houses, and a few astronomically expensive properties. Describing the average housing price in a city using the median instead of the mean statistic ensures that these few extremely expensive (and certainly atypical) properties don’t skew the overall average price to a higher value.

Created with GeoGebra by Vitor Nunes

Interactivity

Try moving the end sides of the chart bars. The values of the f_i column (absolute frequencies) are changed and the median is recalculated.

Statistics

Statistics provide us with the necessary techniques to be able to extract information from a set of data. These data are often presented "raw" or "incomplete" in that they give us useful information about the problem under study but do not highlight any of its important aspects. Thus, the goal of statistics is to extract information from the data to gain a better understanding of the situations they represent. Some statistical practices include, for example, the planning, aggregation and interpretation of observations. Your goal is always to produce the best possible information from the available data. This information is often vital in making important decisions!