Interpreting a Class Test Score Table
A mathematics teacher records marks out of 50 for two sections. Section A (30 students): mean 32, median 34, range 41, with 4 students below 15. Section B (25 students): mean 31, median 26, range 44, with 9 students below 15. The head teacher sees that the means are almost equal and proposes to give both sections the same remedial worksheet. A guardian of a Section B student complains that Section B is being treated unfairly because its median is lower. The teacher must explain what the statistics show and decide how to use the two class periods available for remedial work.
1. Explain what the mean, median and range show about each section, and judge whether the head teacher's proposal is sound.
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The means (32 and 31) are close, but the mean hides the shape of each distribution. Section A: median 34 is above the mean 32, so the scores are pulled down by a few low results - a left-skewed pattern. Only 4 students are below 15. Section B: median 26 is well below the mean 31, so a group of high scorers is pulling the mean up while most students sit lower - a right-skewed pattern. Nine students are below 15, more than double Section A's count. The ranges are similar (41 and 44), so spread alone does not separate them. The head teacher's proposal is therefore not sound: equal means do not mean equal needs. Section A needs help for a small group of weak students; Section B needs whole-class consolidation of basics for a large weak group. The guardian's complaint is partly right - Section B's typical student is weaker - but the remedy should differ by section, not be identical.
2. Design a plan for the two available class periods that uses the statistics, and state what evidence would show it worked.
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Section A, period 1: whole-class quick review, then pair the 4 students below 15 with stronger peers for targeted practice on the specific errors found in their scripts. Section A, period 2: short re-test on those topics. Section B, period 1: re-teach the two or three core skills that most of the 9 weak students missed, using worked examples, since the low median shows the difficulty is widespread. Section B, period 2: guided practice with the teacher circulating, plus a short diagnostic quiz. Evidence of success: for Section A, the 4 weak students move above 15 on the re-test; for Section B, the median rises and the number below 15 falls. The teacher should record both the mean and the median after the re-test, because a rise in mean alone could come from the top students and hide unchanged weak performance.
3. A colleague says: 'Just compare the means; the rest is extra detail.' Respond with a concrete example from this case.
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The case itself is the counter-example. Both means are about 31–32, so a mean-only comparison says the sections are the same. But Section B has 9 students below 15 against Section A's 4, and Section B's median is 26 against 34. Those two facts change the teaching plan completely: Section A needs a small-group fix, Section B needs whole-class re-teaching. A mean can be pulled up by a few high scores, which is exactly what is happening in Section B. The median shows where the typical student stands, and the count below 15 shows how many need help. Using only the mean would waste both class periods on the wrong remedy and leave the weakest students behind.