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Year 9AC9M9ST03

Comparing Multiple Data Sets

Represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures. Plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions.

Two data sets are compared on three things: centre, spread and shape. An outlier moves some measures and barely touches others.

Method

Always compare all three
centre⋅spread⋅shape\text{centre} \cdot \text{spread} \cdot \text{shape}
One alone describes very little.
Outliers move the mean, not the median
The median is resistant. The mean is not.
Outliers hit the range hard
The range depends only on the extremes.
Use the same scale for both sets
Otherwise the comparison is meaningless.
Say how strong the evidence is
A small sample supports a weak conclusion at best.

Worked example

e.g. Class A: 6,7,7,8,9. Class B: 2,7,7,7,22. Compare them.\text{Class A: } 6,7,7,8,9. \text{ Class B: } 2,7,7,7,22. \text{ Compare them.}
  1. Find each mean.A:7,4B:9,0A: 7{,}4 \qquad B: 9{,}0
  2. Find each median.A:7B:7A: 7 \qquad B: 7
  3. Find each range.A:3B:20A: 3 \qquad B: 20
  4. Note which measure moved. The mean did; the median did not.22 is an outlier\text{22 is an outlier}
  5. Describe centre, spread and shape together.same median, far wider spread in B\text{same median, far wider spread in B}
  6. State the evidence strength.n=5 each — too small for a firm conclusionn = 5 \text{ each — too small for a firm conclusion}

Practice

Compare centre, spread and shape. Then say how strong the evidence is.

1
Find the range of 4,9,6,15,8\text{Find the range of } 4,9,6,15,8
Answer1111
2
Which is resistant to outliers, mean or median?\text{Which is resistant to outliers, mean or median?}
AnswerThe median.\text{The median.}
3
Two sets share a median but ranges are 3 and 30. Comment.\text{Two sets share a median but ranges are 3 and 30. Comment.}
AnswerSame typical value, very different consistency.\text{Same typical value, very different consistency.}
4
Removing an outlier: which changes more, mean or range?\text{Removing an outlier: which changes more, mean or range?}
AnswerBoth change a lot; the median barely moves.\text{Both change a lot; the median barely moves.}
5
Why plot two sets on the same scale?\text{Why plot two sets on the same scale?}
AnswerDifferent scales make the comparison meaningless.\text{Different scales make the comparison meaningless.}
6
You sampled 8 students. How strong is your conclusion?\text{You sampled 8 students. How strong is your conclusion?}
AnswerWeak. Report it as tentative.\text{Weak. Report it as tentative.}
Next step
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