The answer
(a)(i) mean \(= 77.1\) g (3 s.f.)
(ii) standard deviation \(= 3.38\) g (3 s.f.)
(b) (1) kiwi fruits are heavier on average (77.1 g vs 65.5 g); (2) kiwi-fruit masses are more consistent / less spread out (SD 3.38 g < 3.83 g)
O-Level E-Math 2025 Paper 1 Question 25 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 25 of the O-Level E-Math 2025 Paper 1. It tests mean of grouped data, in the Central tendency & dispersion area. It is worth 4 marks: (a)(i) 1 + (ii) 1, (b) 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.
Use the interval midpoints: \(72.5,\ 76,\ 78,\ 80,\ 83\) with frequencies \(8, 8, 7, 5, 4\) (total \(N = 32\)).
(a)(i) Mean \(= \dfrac{\sum fx}{N} = \dfrac{8(72.5) + 8(76) + 7(78) + 5(80) + 4(83)}{32} = \dfrac{2466}{32} = 77.06\ldots = 77.1\) g (3 s.f.).
(ii) Standard deviation \(= \sqrt{\dfrac{\sum fx^2}{N} - \bar{x}^2}\). Here \(\sum fx^2 = 8(72.5^2) + 8(76^2) + 7(78^2) + 5(80^2) + 4(83^2) = 190\,402.5\). So s.d. \(= \sqrt{\dfrac{190\,402.5}{32} - 77.0625^2} = \sqrt{5950.08 - 5938.63} = \sqrt{11.44} = 3.38\) g (3 s.f.).
(b) Averages: the kiwi fruits have a higher mean mass (\(77.1\) g) than the plums (\(65.5\) g), so on average the kiwi fruits are heavier. Distributions: the kiwi fruits have a smaller standard deviation (\(3.38\) g \(< 3.83\) g), so their masses are more consistent / less spread out than the plums'.
Answer: (a)(i) mean \(= 77.1\) g (3 s.f.)
(ii) standard deviation \(= 3.38\) g (3 s.f.)
(b) (1) kiwi fruits are heavier on average (77.1 g vs 65.5 g); (2) kiwi-fruit masses are more consistent / less spread out (SD 3.38 g < 3.83 g)
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 mean of grouped data question from Central tendency & dispersion, worth 4 marks: (a)(i) 1 + (ii) 1, (b) 2.
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