Chapter 12: Tales by Dots and Lines
Numbers by themselves rarely speak. But a column of marks turned into a dot plot, or a year of temperatures drawn as a line graph, suddenly tells a story , a heat wave in June, a class that mostly scores around the same mark, an outlier student who runs much faster than the rest.
In this chapter we revisit the mean and the median that you met last year, but from a fresh angle: the mean becomes a balance point on a number line, and the median becomes the middle marker that splits the data in two equal halves. We see how these two centres respond differently when we add, remove, or change a value.
We then learn how a spreadsheet can do the arithmetic for us , typing =AVERAGE(B3:G3) is a lot quicker than adding seven numbers by hand. Finally we move from dot plots to line graphs, which are the natural way to show how something changes over time.
By the end you will be able to compute, compare, and interpret the mean and the median, read dot plots and line graphs, and describe what they reveal , and what they hide.
What's inside
- Mean as a balance point , distances from the mean on the LHS equal distances on the RHS.
- Median and what shifts it , the middle value, and how adding/removing data changes (or doesn't change) it.
- Dot plots , turning a list of values into a visual picture.
- Spreadsheets for data , cells, ranges, and the
SUMandAVERAGEformulae. - Line graphs , showing change over time and reading trends.
Key results
| Idea | Formula / fact |
|---|---|
| Arithmetic mean | |
| Sum from mean | |
| Mean balance | sum of distances below the mean sum of distances above |
| Median (odd ) | the middle value of the sorted list |
| Median (even ) | average of the two middle values |
Spreadsheet formulae. =SUM(B3:G3) adds cells through . =AVERAGE(B3:G3) returns the mean.
How to read this chapter
For every plot you meet, first ask what is on the axes and how the data was collected. Only then read off trends. The same number can tell very different stories depending on the picture you draw with it.