Middle school maths, year 1 · unit 8
Organising and Reading Data
Hear "the average pocket money in our class is ten thousand won" and you assume everyone gets about that. But if one person gets a great deal, the average is easily fooled. This unit is about boiling many numbers down to one, and drawing them so they can be seen at a glance. We start by lining up cards.
Line them up and the middle shows
A board to arrangeThese cards show some friends' pocket money. Drag them into order, smallest first. The value that lands in the middle stands for the group.
The most common one stands for the rest
A board to arrangeA shoe-shop owner does not care about the average size, only the size that sells most. Drag the cards and stack matching ones together.
Group into intervals and a shape appears
A board to adjustReading twenty travel times one by one is dizzying. Group them into 10-minute intervals and stand them up as bars.
Different totals? Compare shares
Joining board6 out of 20, or 10 out of 40: which is the bigger share? Compare by dividing each count by its total.
Try it yourself
Use what you found on the boards. The numbers change every time and the easy questions come first. Get three right and the lamp lights.
What to take away from this unit
- A single value standing for a whole set of data is a representative value: the mean, the median or the mode.
- With the data in order, the middle value is the median; with an even number of values, the mean of the middle two. When there is an unusually big or small value, the median represents the data better than the mean.
- The most frequent value is the mode. It works for data that are not numbers, and there can be more than one.
- Split the data into intervals (classes), count how many fall in each (frequency), and you have a frequency table. Drawn as bars it is a histogram; joining the middles of the bar tops gives a frequency polygon.
- Relative frequency = frequency ÷ total frequency. They add up to 1. Compare groups of different sizes by relative frequency.