What is dispersion?
Dispersion describes how spread out a set of data is. Two data sets can share the same mean yet look very different: one may be tightly clustered while the other is widely scattered. A measure of central tendency (mean, median, mode) alone cannot tell them apart, so we also study dispersion.
- Small dispersion means the values are close together (consistent).
- Large dispersion means the values are widely spread (variable).
- If every value is identical, the dispersion is zero.
Stem-and-leaf plot
A stem-and-leaf plot organises data while keeping the actual values. Each number is split into a stem (the leading digits) and a leaf (the final digit). A key such as $1\,|\,2 = 12$ tells you how to read it.
Example
Stem | Leaf
1 | 2 5 8
2 | 0 3 3 7
3 | 1 4 (Key: $1\,|\,2 = 12$)
There are $3+4+2 = 9$ values. The smallest is $12$ and the largest is $34$. Unlike a bar chart, the original data is not lost.
Dot plot
A dot plot shows each data value as one dot above a number line. Stacked dots reveal which values occur most often and where the data clusters or spreads.
Comparing spread
To compare two data sets, look at how far the values reach across the line. The set whose values stretch over a wider interval has the greater dispersion.
Remember
A stem-and-leaf plot keeps every original value; a dot plot shows each value as a dot. Both let you compare the spread of two sets at a glance.