Mode, median and range · Usually met around P5
The range
Largest − smallest.
How to do it
Method
Largest − smallest
6, 14, 9, 3, 11: 14 − 3 = 11
Another way
Distance on a number line
From 3 to 14: 11 steps
In full
Range = largest − smallest: it says how spread out the data are. To find the largest and smallest, look at all the data, not just the first and last written; sort first and the two ends are the smallest and largest. Comparing two sets: the one with the bigger range is more spread out; the smaller range is closer together, more consistent. Or mark the data on a number line and see how far the leftmost is from the rightmost.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Ming swims 50 m five times; the times (seconds) are 35.1, 32.9, 36.4, 33, 34.5. What is the range of the times in seconds?
Show the answer and working
Answer: 3.5 s
Slowest 36.4 s, fastest 32.9 s: 36.4 − 32.9 = 3.5 s.
Example 2
Data: 16, 1, 24, 16, 16, 8. The range is 24.
True or false?
Show the answer and working
Answer: False
Range = largest − smallest = 24 − 1 = 23.
Example 3
Data: 18, 16, 25 and □, where □ is bigger than the other three. The range is 11. What is □?
Show the answer and working
Answer: 27
□ is the largest and 16 the smallest: □ − 16 = 11, so □ = 16 + 11 = 27.
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