Two groups can share a mean and still have a different spread
See how far the data sits from the mean (its deviation), find out why variance and standard deviation β the average of squared deviations β matter, and see how "spread," something the mean alone can't tell you, gets turned into a number.
The mean is a value that represents the data, but it doesn't tell you how tightly the data is clustered around the mean, or how widely it's spread out. That's why we need the concept of deviation β how far each data value sits from the mean.
Simply add up all the deviations, and you always get 0 (because values above and below the mean cancel each other out). So instead, we square the deviations and average them to get the variance, and take the square root of the variance to bring it back to the original units β that's the standard deviation. The larger the standard deviation, the more widely the data is scattered from the mean.
Even two classes with the same average test score can have a large standard deviation, meaning a big gap between the strong and struggling students. Use the sliders to change the data values and see directly how the deviation and standard deviation change.
Change the data values with the 5 sliders. The distance from each point to the mean (the dashed line) is its deviation. Since simply adding up the deviations always gives 0, we represent the spread with the average of the squared deviations (the variance) and its square root (the standard deviation).
Variance = average of (deviation)Β² Β· Standard deviation = βvariance
Say two classes' test scores both have a mean of exactly 70. Use the slider to change Class B's "spread," and see just how different the situation is when the mean is the same but the standard deviation differs.