What this lesson teaches
I can organise fieldwork data and analyse its patterns with counts, averages and comparisons.
Syllabus K226, Topic 1.3, Key Question 3. How to process and analyse data?
I can read maps, graphs, photographs and texts, and separate what they show from what they suggest.
Syllabus K226, Topic 1.3, Key Question 4 (part). How to present findings?
Make a guess
Five journey times are 2, 4, 4, 6 and 29 minutes. Which number best shows a typical journey?
- 9 minutes, the mean of the five.
- 29 minutes, the longest journey.
- 2 minutes, because it is the quickest.
- 4 minutes, the middle value.
Show the answer
4 minutes, the middle value.
The single 29-minute trip pulls the mean up to 9 minutes. The median, 4, sits in the middle and is not dragged up by one unusual value.
Pick the statistic that fits your data, state its unit and total, and check whether unusual values change the picture.
A frequency is a count. If 12 of 20 people walk to a park, that is 12 / 20 x 100 = 60%. The 20 is the denominator, the total you compare against. The result describes the people asked, not all residents. Check for missing answers first, and note that questions allowing several answers may not add to 100%.
Take the made-up journey times 5, 5, 10, 15 and 40 minutes. The mean adds them and divides by how many there are: 75 / 5 = 15 minutes. The median is the middle value when in order: 10 minutes. With an even number of values, the median is the mean of the two middle ones. The mode is the most common value: 5 minutes.
The 40-minute journey pulls the mean above the median. So here the median may better show a typical journey, while the mean uses every value. Do not delete an unusual value just because it is different. Check whether it is a mistake or real. You can find the mode of categories, like bus or car, but not their mean.
- Mean
- Add all values, then divide by how many.
- Median
- The middle value, in order.
- Mode
- The most common value.
Step by step
Check the data
Units, missing values and the right total.
Calculate clearly
Show your working.
Interpret
Say what it shows, and whether an odd value affects it.
Worked example: Percentage points or per cent?
If walking rises from 40% to 60%, that is a rise of 20 percentage points. Compared with the start, it is a 50% increase: (60 - 40) / 40 x 100. Say which one you mean.
Watch out for this
An average shows everyone had the same experience.
An average summarises spread-out values. Mention important exceptions.
Check your understanding
For journey times 5, 5, 10, 15 and 40 minutes, which statement is correct?
- The median is 15, because the median and the mean are the same here.
- The mode is 40, because the mode is the value that stands out the most.
- The mean is 15 and the median 10; the long trip raises the mean.
Show the answer
The mean is 15 and the median 10; the long trip raises the mean.
Yes. The 40-minute value pulls the mean up.
Check your understanding
Journey times are 5, 5, 10, 15 and 40 minutes. Which average best shows a typical journey?
- The mean, 15 minutes, because it is the average that uses every value.
- The median, 10 minutes, as the 40-minute trip pulls the mean up.
- The mode, 5 minutes, because it appears most.
Show the answer
The median, 10 minutes, as the 40-minute trip pulls the mean up.
An extreme value distorts the mean.