Same average, different days
Two bus routes both have an average lateness of 6 minutes. On route A every bus is 5, 6 or 7 minutes late. On route B buses run from 0 to 15 minutes late.
An average hides this. You need a way to measure how spread out the data is.
Key words
| Word | What it means |
|---|---|
| Dispersion | how spread out the values are |
| Minimum | the smallest value |
| Maximum | the largest value |
| Range | the maximum take away the minimum |
| Frequency | how many times a value appears |
| Frequency count | a list of each value with its frequency |
| Database | an organised store of tables that you can ask questions |
| SQL | the language used to ask a database for data |
The cells students fill in are left blank in this preview.
By the end of this lesson
Note
I can find the minimum, maximum and range, and build a frequency count, and say what each tells me.
Starter
Have a go
Starter
3 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.
Worked example: seven late pupils
| Measure | Working | Result |
|---|---|---|
| Minutes late | Amy 5, Bo 2, Cy 5, Di 9, Eli 2, Flo 5, Gus 12 | |
| Minimum | The smallest value | 2 |
| Maximum | The largest value | 12 |
| Range | 12 take away 2 | 10 |
The cells students fill in are left blank in this preview.
What range tells you
The range is one number for the whole spread. A small range means the values are close together. A large range means they are far apart.
Range uses only the two ends, so one outlier changes it a lot. It is quick, but it is a rough measure.
Try it: a frequency count in SQL
SELECT minutes, COUNT(*) AS pupils
FROM late
GROUP BY minutes
ORDER BY minutes;
-- Minimum, maximum and range in one query.
SELECT MIN(minutes) AS fastest, MAX(minutes) AS slowest,
MAX(minutes) - MIN(minutes) AS spread
FROM late;
A frequency count as a table
| Minutes late | Frequency | Bar |
|---|---|---|
| 2 | 2 | ## |
| 5 | 3 | ### |
| 9 | 1 | # |
| 12 | 1 | # |
The cells students fill in are left blank in this preview.
A chart of frequencies
Important
A frequency count is the table behind a bar chart or a histogram. This platform has no charting tool, so the bars above are text. In a spreadsheet you would draw the chart from the same table.