Reading the Shape of Data

Picture the data set 2, 2, 4, 6, 6 as dots on a number line. The dots balance evenly around the middle value, 4, so this shape is called symmetricA distribution shape where the data is evenly balanced on both sides of the center.. Now picture 1, 2, 2, 3, 20. Almost every dot bunches up near 1 through 3, except one value way out at 20 that stretches a long tail to the right, this shape is called skewA distribution shape where most of the data bunches on one side and a tail stretches out toward the other side.ed, and the lonely value at 20 is an outlierA data value that is much greater or much less than the rest of the values in a data set.: a value much greater or much less than the rest.

Some data sets don't bunch up anywhere at all. The set 1, 2, 3, 4, 5 spreads evenly across the range with no clear peak, so it's called uniformA distribution shape where the data values are spread out fairly evenly across the range, with no clear peak.. And some data sets have two separate clusters, like 2, 2, 7, 7, 9, which peaks once near 2 and again near 7, a shape called bimodalA distribution shape with two separate peaks, meaning the data clusters around two different values.. Here's why shape matters: an outlier like the 20 above can drag some measures of center away from where most of the data actually lives, so for a skewed set with an outlier, the median usually describes the data better than a measure that gets pulled toward the tail. But for a bimodal set like 2, 2, 7, 7, 9, naming the most frequent value, the mode, can be more useful, because it names exactly where each cluster sits.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.