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The five-number summary of a dataset is given - HSC - SSCE Mathematics Standard - Question 17 - 2021 - Paper 1

Question 17

The five-number summary of a dataset is given. Lowest score = 1 Lower quartile (Q1) = 4 Median (Q2) = 7 Upper quartile (Q3) = 10 Highest score = 20 Is 20 an outlie... show full transcript

Worked Solution & Example Answer:The five-number summary of a dataset is given - HSC - SSCE Mathematics Standard - Question 17 - 2021 - Paper 1

Step 1

Calculate the Interquartile Range (IQR)

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Answer

The interquartile range (IQR) is calculated as follows:

$IQR = Q3 - Q1$

Substituting the values:

$IQR = 10 - 4 = 6$

Step 2

Determine the Outlier Boundaries

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Answer

Using the IQR, we can find the upper boundary to identify outliers. The formula is:

$Q3 + 1.5 \times IQR$

Substituting the values:

$Q3 + 1.5 \times IQR = 10 + 1.5 \times 6 = 10 + 9 = 19$

Step 3

Justify if 20 is an Outlier

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Answer

Since 20 exceeds the upper boundary of 19, we conclude:

20 is an outlier as it is greater than 19.

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