Home / IB DP Math AI: Topic: SL 4.1: Concepts of population, sample: IB style Questions HL Paper 2

IB DP Math AI: Topic: SL 4.1: Concepts of population, sample: IB style Questions HL Paper 2

Question

200 people were asked the amount of time T (minutes) they had spent in the supermarket. The results are represented in the table below.

a.State if the data is discrete or continuous.[1]

b.State the modal group.[1]

c.Write down the midpoint of the interval 10 < T ≤ 20 .[1]

d.Use your graphic display calculator to find an estimate for

(i) the mean;

(ii) the standard deviation.[3]

e.The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.

Write down the value of

(i) q;

(ii) r.[2]

f.The results are represented in the cumulative frequency table below, with upper class boundaries of 10, 20, 30, 40, 50.

On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 10 minutes (T) on the horizontal axis and 1 cm to represent 10 people on the vertical axis.[4]

g.Use your graph from part (f) to estimate

(i) the median;

(ii) the 90th percentile of the results;

(iii) the number of people who shopped at the supermarket for more than 15 minutes.[6]

▶️Answer/Explanation

Markscheme

continuous     (A1)[1 mark]

a.

20 < T ≤ 30     (A1)[1 mark]

b.

15     (A1)[1 mark]

c.

(i) 21.5     (G2)

(ii) 9.21 (9.20597…)     (G1) [3 marks]

d.

(i) q = 194     (A1)

(ii) r = 200     (A1)[2 marks]

e.