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One Cumulative Frequency Curve To Rule Them All

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Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 1:10 pm (Singapore time)

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Prepare for MODERATION!!! Rejoice! For our scouts bring forth great tidings from the frontline once more!

An awesome sight to behold, as entire divisions of our enemy were annihilated by the great phalanxes of our brave warriors, with their remnants fleeing even as we speak.

Long-feared nightmares in the likes of Relative Velocity and Kinematics finally emerged from the enemy’s ranks but were swiftly slayed, and their spirits banished to the infernal lair from where they came. Woe to the schools that deprive their charges the chance to partake in the slaying of these mighty beasts!

So in the end, there were no Level 99 fireballs. As our alchemists and mages began preparing their chemical spells for their battle later today, amidst the self-congratulations and widespread burning of A-Maths notes, some, though, are beginning to question the ease of this victory.

With the exact mechanics of allocating the spoils of war veiled in secrecy by the shady War Council, and with a major chunk of the top grades almost certain to be taken up by the foreign cyborg mercenaries, an uneasiness exists within our ranks.

Yes Miss Loi’s old adage

85% for A-Maths and 90% for E-Maths to get an A1!

looks ominously true now.

For a hypothetical look at the inner workings of the War Council, and to let you practise something that is almost certain to appear in your upcoming E-Maths Paper 1, take a sample of our students from yesterday’s battles:

120 candidates took a Mathematics examination which consists of two papers. Each paper was marked out of 100. The diagram shows,on the same axes, the cumulative frequency curves for Paper 1 and Paper 2.

Cumulative Frequency Graph

Use the graph for Paper 2 to estimate

  1. the median mark.
  2. the inter-quartile range.
  3. the number of candidates who scored more than 70 marks.
  4. the pass mark such that 60% of the pupils will pass the examination.
  5. the minimum mark required to gain a distinction if the top 5% of the pupils are awarded a distinction.

State, with reason, which was the more difficult paper.

Yes even the War Council rely on that little bit of E-Maths to seal your fate.

Cumulative Frequency Summary The chart on the right summarizes all you need for this question. But in the heat of battle it’s sometimes easy to forget that quartiles are determined by the percentages on the cumulative frequency axis, and that their values are actually taken from the horizontal axis.

Parts 4 and 5 of the question once again involve that additional topic not found in your textbook called common sense, which we usually assume that members of the War Council possess. Ask yourself these: Will you pass your exam if you scored zero? On the contrary, will you fail your exam if you scored 100 marks?

Now, say Hi and wave to yourself on the vertical axis!

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