Data & the mean

How many messages do you send per day? How long does it take you to get to school? On any single day that varies, but over many days a pattern appears. That's what data is for: you collect numbers, display them clearly, and condense them into one figure you can talk about.

Collecting data and showing it as bars

A list like 12, 15, 9, 16 says little at first. Draw one bar per value and you see immediately: where do most values sit, and which ones stand out above or below? A bar chart turns a list of numbers into a picture you can read at a glance.

Mean and range

The mean answers the question: how much would it be if everyone had the same amount? You calculate it like this: the sum of all values divided by how many there are. For 4, 6, and 8 that's (4 + 6 + 8) : 3 = 6. The range, on the other hand, measures how far apart the values lie: largest value minus smallest value. For 4, 6, and 8 it's 8 − 4 = 4. Two data sets can share the same mean and still spread completely differently.

When the mean misleads

Four friends own 2, 3, 3, and 4 games, and a fifth owns 28. The mean is (2 + 3 + 3 + 4 + 28) : 5 = 8, yet nobody in the group owns anywhere near 8 games. The 28 is an outlier, a value that lies far away from all the others. A single value like that pulls the mean strongly towards itself. That's when the median helps: you sort all values and take the middle one. Sorted, the list reads 2, 3, 3, 4, 28. The median is therefore 3, and that describes the group far more honestly. With an even number of values the middle falls between two values, so you take the mean of those two.