IB DP Maths Topic 5.1 Grouped data: use of mid-interval values for calculations; interval width SL Paper 1

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Question

The following box-and-whisker plot shows the number of text messages sent by students in a school on a particular day.

Find the value of the interquartile range.

[2]

One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.

[4]

Answer/Explanation

recognizing Q₁ or Q₃ (seen anywhere) (M1)

eg 4,11 , indicated on diagram

IQR = 7 A1 N2

[2 marks]

recognizing the need to find 1.5 IQR (M1)

eg 1.5 × IQR, 1.5 × 7

valid approach to find k (M1)

eg 10.5 + 11, 1.5 × IQR + Q₃

21.5 (A1)

k = 22 A1 N3

Note: If no working shown, award N2 for an answer of 21.5.

[4 marks]