|How many smarties do you think are on this poster? How many blue smarties are on this poster?|
|Can you use the frames provided to estimate the total number of smarties? Which frame do you think is the best choice?|
|Survey as many people as possible on what they think. What are the range of answers? Using your data, what is your best estimate?|
If we count the number of smarties inside a frame, and then work out how many frames cover the poster, we can estimate the total number of smarties.
Or we can count how many smarties are inside the frame, and how many of them are blue smarties, and estimate the proportion of blue smarties.
It is easier to work out how many frames cover the picture when the frame is square or a triangle.
Another way to estimate the total number is to take a survey of people’s best guesses, and using the average as your estimate. This works because some of these guesses will be too high, and some will be too low, but if we’re lucky the errors will cancel out. This is called Wisdom of the Crowds.
In 1906, British statistician Francis Galton attended a county fair. One stall had a contest to guess the weight of an ox and win a prize. 800 people entered the competition, secretly writing their best guess on a piece of paper and submitting their answer. Galton noticed that the average of these guesses was almost exactly correct.
Sometimes we want to count large numbers. Maybe you are a factory making thousands of sweets a day, or want to know how many people in the country wear glasses. Counting large numbers can be difficult, or expensive. So it’s often easier, and cheaper, to take a small sample and then estimate how many things there are in total.
Maths at Home
Try the wisdom of the crowds experiment at home. For example, ask people to guess how many jelly beans are in a jar. The more people you ask the better. What was the largest guess? What was the smallest guess? Was the average close to the correct answer?