Year 10 · Statistics · 2 minutes
Mean, median and mode
Mean shares it out, median sits in the middle, mode is most common.
Key terms
- Mean
- The total of all the values shared out equally between everyone, found by adding up and dividing.
- Median
- The middle value once the data is in order from smallest to largest.
- Mode
- The value that turns up most often in the data.
- Outlier
- A value far bigger or smaller than the rest, which can drag the mean a long way.
- Data
- The values collected, such as the hours of screen time that nine students reported.
Transcript
We asked nine Year Tens: how many hours of screen time did you have last weekend? Here are their answers. So what's a typical answer? Statistics gives us three ways to say it.
First, the mean. Add up every value: forty five hours in total. Now share that total out equally, between all nine students. Forty five divided by nine is five. The mean is five hours.
Next, the median. Put the values in order, from smallest to largest. The median is the one in the middle. With nine values, that's the fifth one: four hours.
Then there's the mode: the most common value. Three hours turns up three times, more than anything else. So the mode is three.
Now a tenth student adds their answer. They binge watched a whole series: twenty five hours! The total jumps to seventy, and seventy divided by ten is seven. The mean slides all the way up to seven.
But look at the median. With ten values, there are two in the middle: four and five. Halfway between them is four and a half. One huge value, and the median hardly moves.
So which one should you use? The mean uses every value, so it works well when the data is balanced. But with an outlier, the median gives a fairer picture. And the mode is great for the most popular choice, like a favourite sport.
So: the mean, add them up and share equally. The median, the middle value, once they're in order. The mode, the most common. And watch out for outliers!
Sources
Every fact in the video, and where it comes from.
- 1britannica.com/topic/mean-median-and-mode
- Mean, median and mode are the three main ways of expressing the average (centre) of a list of numbers; the arithmetic mean is the sum of the values divided by how many values there are.
- The median is the middle value when the values are arranged in order; with an even number of values it is the mean of the two middle values.
- The mode is the value that occurs most often.
- 2topdrawer.aamt.edu.au/Statistics/Activities/Awareness-of-outliers
- An outlier pulls the mean strongly while the median is much less affected, so the median often better represents skewed data.
Teaching this next week?
Kuraplan turns this topic into a lesson plan, slides and a worksheet for your class in about a minute.
Plan a lesson on this topic
