The answer
(a) \(128\) grams
(b) \(x = 7\)
(c) apples are heavier on average and more spread out (see below)
O-Level E-Math 2018 Paper 1 Question 19 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 19 of the O-Level E-Math 2018 Paper 1. It tests median from an ordered list, in the Data handling (stem-and-leaf) 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.
Reading the apple leaves (innermost digit is the units): \(92, 95, 100, 101, 102, 108, 110, 110, 115, 116, 119, 122, 123, 124, 127, 129, 130, 132, 132, 135, 136, 138, 144, 146, 148, 148, 149, 153, 159, 159\) (30 values).
(a) With 30 values the median is the mean of the 15th and 16th: \(\dfrac{127 + 129}{2} = 128\) grams.
(b) The bananas run from a smallest mass of \(103\) g (stem 10, leaf 3). A range of \(44\) g means the largest banana is \(103 + 44 = 147\) g. The largest banana is on stem 14 with leaf \(x\), i.e. mass \(140 + x\), so \(140 + x = 147 \Rightarrow x = 7\).
(c) Two valid comparisons: (i) the apples are heavier on average, with median \(128\) g against the bananas' median of \(125\) g (the bananas' 13th value); (ii) the apples are more spread out, with range \(159 - 92 = 67\) g against the bananas' range of \(44\) g. (Any two correct comparisons of average and/or spread are acceptable.)
Answer: (a) \(128\) grams
(b) \(x = 7\)
(c) apples are heavier on average and more spread out (see below)
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 median from an ordered list question from Data handling (stem-and-leaf), worth 4 marks: 1 + 1 + 2.
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