Comparing Two Data Sets
Interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape.
Read this first
Compare the mode, the range and the shape. All three, every time.
Two sets can share a mode and still be very different.
Words you need
- Mode
- The most common value.
- Range
- The biggest value take away the smallest.
- Shape
- Where most of the data sits.
Worked example
e.g. Class A scores 6,7,7,8,9. Class B scores 2,7,7,7,14. Compare them.
- Find the mode of each. Both are 7.
- Find the range of A. 9 - 6 = 3.
- Find the range of B. 14 - 2 = 12.
- Same mode, very different spread.
- Class A is more consistent. Class B is spread out.
Never compare on one measure alone. The mode can hide everything else.
Practice
The pictures fade as you go. By the last few you are on your own.
1Which class is more spread out?with a picture
AnswerClass B. Its range is much bigger.
2Do the two classes have the same mode?with a picture
AnswerYes. Both are 7.
3Find the range of 4, 9, 6, 15, 8.with a hint
Need a hint?
Biggest take away smallest.
Answer11.
4Two sets have the same range. Must they look the same?with a hint
Need a hint?
Think about where the middle values sit.
AnswerNo. The shape can differ.
5Find the mode of 5, 8, 5, 9, 5.on your own
Answer5.
6Set A range 2, set B range 20. Which is more consistent?on your own
AnswerSet A.
7Why report shape as well as mode?on your own
AnswerThe mode alone does not show how the data is spread.
Think about it
1
Why is range useful when the modes match?
One good answerIt shows how spread out each set is.
2
What does a small range tell you?
One good answerThe values are all close together.
Common mistakes
Comparing only the modes.
Look at range and shape too.
Thinking a big range means big values.
It only means the values are far apart.