Data Analysis, SM-Bank 051

Ms Granger measured and recorded the heights of all the students in her class, to the nearest centimetre.

She made a dot plot to show the heights of these 32 children.

Student Heights (nearest cm)

What fraction of the students' heights are greater than 145 centimetres and less than 150? (2 marks)

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What is the range of the heights? (1 mark)
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What is the median of the heights? (1 mark)
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What would the median be if a new student arrived with a height of 135 cm? (1 mark)
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Show Answers Only

a. \(\dfrac{1}{4}\)

b. \(18\)

c. \(147.5\ \text{cm}\)

d. \(147\ \text{cm}\)

Show Worked Solution

a.	\(\text{Fraction}\)	\(=\dfrac{\text{Students with height 145 – 150}}{\text{Total students}}\)
		\(=\dfrac{8}{32}\)
		\(=\dfrac{1}{4}\)

\(\text{(Note students with heights of 145 or 150 are not included)}\)

b. \(\text{Range}=154-136=18\)

c.	\(\text{Median}\)	\(=\dfrac{\text{16th score + 17th score}}{\text{2}}\)
		\(=\dfrac{147+148}{2}\)
		\(=147.5\ \text{cm}\)

d.	\(\text{Median }\)	\(=\text{ 17th score}\)
		\(=147\ \text{cm}\)