The answer
(a) \(\approx 39.6\) min
(b) \(\approx 9.42\) min
(c) \(\approx 32\)
O-Level E-Math 2017 Paper 1 Question 16 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 16 of the O-Level E-Math 2017 Paper 1. It tests estimated mean from a grouped table, in the Averages & spread (grouped data) / pie charts area. It is worth 4 marks: 1 + 1 + 2. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
Using midpoints \(25, 35, 45, 55, 65\) with frequencies \(28, 84, 62, 21, 5\) (total \(200\)):
(a) Mean \(= \dfrac{\sum fx}{\sum f} = \dfrac{25(28) + 35(84) + 45(62) + 55(21) + 65(5)}{200} = \dfrac{7910}{200} = 39.55 \approx 39.6\) min.
(b) Standard deviation \(= \sqrt{\dfrac{\sum fx^2}{\sum f} - \bar{x}^2}\). Here \(\sum fx^2 = 25^2(28) + 35^2(84) + 45^2(62) + 55^2(21) + 65^2(5) = 330600\), so \[\text{SD} = \sqrt{\frac{330600}{200} - 39.55^2} = \sqrt{1653 - 1564.2025} = \sqrt{88.7975} \approx 9.42 \text{ min}.\]
(c) The pie chart sectors are proportional to the number of adults, so the count in a sector is proportional to its angle. Measuring the "21 to 30" sector gives an angle of about \(99^{\circ}\) for \(44\) adults. The "41 to 60" sector measures about \(72^{\circ}\), so the number aged 41 to 60 is about \(44 \times \dfrac{72^{\circ}}{99^{\circ}} \approx 32\). (Pie-chart angles are measured from the printed reprint, so this is a best estimate; accept about 30 to 34.)
Answer: (a) \(\approx 39.6\) min
(b) \(\approx 9.42\) min
(c) \(\approx 32\)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a estimated mean from a grouped table question from Averages & spread (grouped data) / pie charts, worth 4 marks: 1 + 1 + 2.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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