Box Plots: WJEC GCSE Numeracy Intermediate November 2019 Unit 1 Q12

Numeracy Intermediate November 2019 Unit 1 Q12

WJECIntermediateCurrent spec7 marksBox Plots Cumulative Frequency

12. On 1st July every year, Trefor estate agents record the time from when a phone rings to when it is answered.
The time taken to answer the phone is recorded in seconds.

Trefor displays the data for their agents to see.
The displays for 1st July 2018 and 1st July 2019 are shown below.

1st July 2018: box plot of time taken to answer the phone in seconds, on a scale from 0 to 120 seconds

1st July 2019: cumulative frequency graph (0 to 80) of time taken to answer the phone, time 0 to 120 seconds

Use the diagrams above to answer the following questions.

(a) What is the range of times taken to answer the phone for 1st July 2018?
Circle your answer. [1]

101 seconds 80 seconds 78 seconds 106 seconds 104 seconds

(b) What is the maximum possible range of times taken to answer the phone for 1st July 2019?
Circle your answer. [1]

86 seconds 106 seconds 80 seconds 56 seconds 83 seconds

(c) The manager of Trefor estate agents claims that there has been an improvement in the median time taken to answer the phone from 1st July 2018 to 1st July 2019.
Is this true?

Yes ☐ No ☐

You must show all your working. [2]

(d) Complete the following statements.

(i) ‘On 1st July 2018, 75% of the phone calls were answered within …………… seconds.’ [1]

(ii) ‘On 1st July 2019, 75% of the phone calls were answered within …………… seconds.’ [2]

Scheme	Marks	Comments
104 seconds	B1

Scheme	Marks	Comments
86 seconds	B1

Mark scheme (c)

Scheme	Marks	Comments
Sight of median 1^st July 2018 78 (seconds) AND Sight of median 1^st July 2019 56 or 57 (seconds) AND States or implies ‘Yes’	B2	Check the diagrams Allow statements without giving medians, e.g. ‘medians are (just) less than 80 and less than 60 respectively’ If medians are stated they must be correct, otherwise possible maximum of B1 B1 for 1 of the medians correct with an appropriate FT interpretation, or both medians correct without correct interpretation or with incorrect interpretation

Mark scheme (d)

Scheme	Marks	Comments
(i) 100 (seconds)	B1
(ii) (0.75 × 80 =) 60 (calls)	M1
72 (seconds)	A1	60 seen in the answer space is awarded M1 A0 If no marks, award SC1 for a misread of the graph implied from sight of answers 66, 76 or an answer between 71 and 73 (excluding 72)