Question 1

Paper 2Medium6 marks

Ridgeway College wants to estimate the usual one-way travel time of all its students. A staff member asks the first 40 students they meet as they leave the cafeteria at lunch. For these responses, the lower quartile is 18 minutes and the upper quartile is 30 minutes. One recorded travel time is 55 minutes.

(a)

Calculate the interquartile range (IQR).

[1]
(b)

Determine whether the travel time of 55 minutes is an outlier. Show a comparison with the nearest quartile.

[2]
(c)

The student confirms that 55 minutes is accurate for their usual journey, which includes a ferry crossing and a transfer. Should this value be removed when summarizing the sample? Justify your answer.

[1]
(d)

Explain one limitation of the staff member’s sampling method and suggest a more suitable sampling method.

[2]

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