Estimating time
How well can you estimate 10 seconds? Investigate with our timing tool.
Age
11 to 14
Challenge level
Problem
How well can you estimate time?
Start by trying to estimate exactly ten seconds:
Full Screen and tablet version
You could have several attempts and then analyse the data from the table. You could collect data from several people to do some interesting comparisons.
Here are some questions you might like to consider:
Are people better at estimating short amounts of time (10 or 15 seconds) or longer time intervals (30 or 60 seconds)?
If a person's first attempt is an over-estimate, do they tend to underestimate on their second go?
If you are better than your partner at estimating 10 seconds, are you more likely to also be better at estimating longer time intervals?
Are older people better at estimating than younger people?
Do people get better at estimating if they practise?
Some people estimate time by reciting or singing something of a specific length, others by counting, others by visualising the hands of a clock...
Which strategies for estimating are most effective?
Is a person who is better at estimating time also likely to be better at estimating angles? Try Estimating Angles.
Does someone who can react faster also judge time intervals better? Try Reaction Timer.
Getting Started
Does it make sense to use averages to see how close someone is to 10 seconds on average?
What else might you need to take into account?
Student Solutions
Well done to everyone who had a go at this problem. Lots of you suggested that a good way of estimating time was to say a certain phrase that lasts around one second over and over again.
Yiyi from Harrow International School in Hong Kong shared these thoughts:
People are usually better at estimating shorter amounts of time such as 10 or 15 seconds than 30 or 60 seconds because if a person is counting too fast or too slow a longer time such as 60sec, it allows them more time to go even faster or slower giving them a wider range of time to do so.
So people that are better at estimating 10 seconds are not always good at estimating a longer time. But there are some that realise they are counting at the wrong pace during the middle therefore count more to the opposite pace (faster to slower / slower to faster).
Normally when the first attempt of a person is over-estimated the second would be under as the person tries to count slower but the pace of counting might change during the middle so it won't always be the opposite of the first attempt. The same with underestimating on the first attempt.
Some people estimate time by saying a word of a specific length. But it depends on the speed that it's said because just saying it does not always give the same time because you could say it faster and slower.
Thanks also to Ahrus, Aliyah, Zahra, Isha, Bilal, Aaqib and Mohammed, all students from Dixons Trinity Academy in Bradford, for their contributions.
Having carried out various experiments they then commented on how they could be improved; they pointed out that next time, to be able to draw reliable conclusions from their experiments, they would want to perform a larger number of trials and use a larger sample of people. They appreciated the value of communicating their results clearly and used averages, tables and graphs. Thank you all.
Teachers' Resources
Why do this problem?
Estimating time is not a new idea for a data gathering exercise, but the tool provided in this problem allows easy collection of data that can be pasted into a spreadsheet, offering an ideal opportunity for some work on using spreadsheets to calculate statistics. See also the problem Reaction Timer.
Possible approach
You may wish to use the data in the problem Half a Minute to introduce the problem.
There are a wide range of questions that can be explored with the tool, and analysis can be performed at lots of different levels, so this is an ideal problem for all ages.
For younger students, you could draw out the idea of averaging repeated trials, and discuss which average might be most appropriate.
Older students might look at moving averages to see whether someone becomes better at estimating.
In order to compare two people's results, it might be necessary to introduce measures of spread - range and interquartile range, and for the oldest students, variance and standard deviation.
If different classes are working on this problem at the same time, there's a great opportunity for sharing data between them, and being able to work on bigger hypotheses like comparing students of different ages. If your school creates a large data set using this tool, please get in touch if you'd like to share it!
You could discuss different strategies that could be used to improve one's performance at estimating particular time intervals (such as reciting something at a steady speed or counting using a phrase exactly one second long). Then the class could design a statistical test to evaluate the different methods.