Home / IBDP Maths SL 4.2 Understanding of box and whisker diagrams AA HL Paper 2- Exam Style Questions

IBDP Maths SL 4.2 Understanding of box and whisker diagrams AA HL Paper 2- Exam Style Questions

IBDP Maths SL 4.2 Understanding of box and whisker diagrams AA HL Paper 2- Exam Style Questions- New Syllabus

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Question

A random sample of nine adults were selected to see whether sleeping well affected their reaction times to a visual stimulus. Each adult’s reaction time was measured twice. The first measurement for reaction time was taken on a morning after the adult had slept well. The second measurement was taken on a morning after the same adult had not slept well. The box and whisker diagrams for the reaction times, measured in seconds, are shown below.

Box-and-whisker diagrams for reaction times

Consider the box and whisker diagram representing the reaction times after sleeping well.

a. State the median reaction time after sleeping well. [1]

b. Verify that the measurement of 0.46 seconds is not an outlier. [3]

c. State why it appears that the mean reaction time is greater than the median reaction time. [1]

Now consider the two box and whisker diagrams.

d. Comment on whether these box and whisker diagrams provide any evidence that might suggest that not sleeping well causes an increase in reaction time. [1]

▶️ Answer/Explanation
Markscheme Solution

a. [1 mark]

The median reaction time after sleeping well is 0.28 (s) (A1).

b. [3 marks]

IQR = 0.35 – 0.27 = 0.08 (s) (A1).
Upper fence: 0.35 + 1.5 × 0.08 = 0.35 + 0.12 = 0.47 (s) (A1).
0.46 < 0.47, so 0.46 (s) is not an outlier (R1).

c. [1 mark]

EITHER
The median is closer to the lower quartile (positively skewed) (R1).
OR
The distribution is positively skewed (R1).
OR
The range of reaction times below the median is smaller than the range of reaction times above the median (R1).

d. [1 mark]

EITHER
The distribution for ‘not sleeping well’ is centred at a higher reaction time (R1).
OR
The median reaction time after not sleeping well is equal to the upper quartile reaction time after sleeping well (R1).
OR
75% of reaction times are <0.35 seconds after sleeping well, compared with 50% after not sleeping well (R1).
OR
The sample size of 9 is too small to draw any conclusions (R1).

Markscheme Answers:

(a) 0.28 (s) (A1)

(b) IQR = 0.08 (s), upper fence = 0.47 (s), 0.46 < 0.47, so not an outlier (A1A1R1)

(c) The distribution is positively skewed (R1)

(d) The median reaction time after not sleeping well is equal to the upper quartile reaction time after sleeping well (R1)

Total [6 marks]

Question

The weekly wages (in dollars) of 80 employees are displayed in the cumulative frequency curve below.

Cumulative frequency curve for weekly wages

a(i). Write down the median weekly wage.

a(ii). Find the interquartile range of the weekly wages. [4]

The box-and-whisker plot below displays the weekly wages of the employees.

Box-and-whisker plot for weekly wages

Write down the value of

b(i). \( a \);

b(ii). \( b \);

b(iii). \( c \). [3]

c. Employees are paid $20 per hour. Find the median number of hours worked per week. [3]

d. Employees are paid $20 per hour. Find the number of employees who work more than 25 hours per week. [5]

▶️ Answer/Explanation
Markscheme Solution

a(i). [1 mark]

Median weekly wage = 400 (dollars) (A1).

a(ii). [3 marks]

Lower quartile = 330 (dollars) (A1).
Upper quartile = 470 (dollars) (A1).
IQR = 470 – 330 = 140 (dollars) (A1).

b(i). [1 mark]

\( a \) = 330 (dollars) (A1).

b(ii). [1 mark]

\( b \) = 400 (dollars) (A1).

b(iii). [1 mark]

\( c \) = 700 (dollars) (A1).

c. [3 marks]

Use hours = wages / rate (M1).
Substitute: \(\frac{400}{20}\) (A1).
Median hours per week = 20 (A1).

d. [5 marks]

Attempt to find wages for 25 hours per week: wages = hours × rate (M1).
Substitute: \( 25 \times 20 \) (A1).
Wages = 500 (dollars) (A1).
From cumulative frequency curve, 65 people earn 500 (dollars) or less (A1).
Number of employees who work more than 25 hours: \( 80 – 65 = 15 \) (A1).

Markscheme Answers:

a(i). 400 (dollars) (A1)

a(ii). IQR = 140 (dollars) (A1A1A1)

b(i). \( a \) = 330 (dollars) (A1)

b(ii). \( b \) = 400 (dollars) (A1)

b(iii). \( c \) = 700 (dollars) (A1)

c. 20 hours (M1A1A1)

d. 15 employees (M1A1A1A1A1)

Total [15 marks]

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