What it shows
Equal weights hung from a numbered beam at the data values balance only when the support is at the mean. Weights at 2, 3 and 7 balance at 4, their mean, and moving one weight from 7 to 13 shifts the balance point to 6, showing how an extreme value pulls the mean.
The science
A beam balances when the turning effects on both sides are equal: the sum of weight times distance on the left equals the sum on the right. With equal weights, this means the total of the distances from the pivot to the weights on the left equals the total on the right, which happens only when the pivot is at the average of the positions. So the mean is the balance point, or centre of mass, of the data. The median, by contrast, only cares about the order, so one far-away weight moves the mean but not the median.
Materials
Cost: under Rs 50. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A straight wooden scale or a 60 cm batten marked 0 to 20
- A triangular block or a pencil fixed to a base as the pivot
- Six identical washers or coins with thread loops
- A nail or hook at every number mark
- A small level or a straight edge
Safety
For this project: An adult must fix the hooks and make sure the beam cannot fall on fingers.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Mark the beam from 0 to 20 at 3 cm intervals and screw a small hook under every mark.
Find the beam's own balance point and check it is at the middle mark, 10; if not, add a lump of clay to one end until it is.
Hang one washer each at 2, 3 and 7 and slide the beam on the pivot until it balances. Read the pivot position: 4.
Check with the formula: (2 + 3 + 7) divided by 3 = 4.
Move the washer at 7 to 13 and find the new balance point: 6, which is (2 + 3 + 13) divided by 3.
Hang washers at 5, 5, 6, 6, 8 and 12 and predict the mean before testing: 42 divided by 6 = 7.
Mark the median of each data set with a coloured peg and show that in the last two cases it did not move as much as the mean.
Write the rule on the display: the mean is where the data balances.
What you should see
The beam balances at 4 for data 2, 3, 7, at 6 when 7 becomes 13, and at 7 for 5, 5, 6, 6, 8, 12, matching the calculated means each time.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why does the beam balance at the mean?
The distances of the weights from the pivot on each side add to the same total only when the pivot is at the average position.
2What happens to the mean if one value becomes very large?
It is pulled towards that value, as the balance point moved from 4 to 6.
3Does the median change when 7 becomes 13?
No. The middle value of 2, 3, 13 is still 3.
4What is the mean of 4, 8 and 9?
7.
Take it further
Hang two washers at one value to show frequency, and find the mean of a frequency table on the beam.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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