GED and HiSET mathematics — data and probability

The last stretch of the mathematics paper is statistics and probability, and it is the part where the arithmetic is easy and the wrong answer is still available. There are no charts anywhere in this set: every data set is written out as a list, and anything a chart would have shown is described in a sentence.

The averages come first, and they are chosen to pull against each other. Five hourly wages — fifteen, fifteen, eighteen, twenty, and a hundred — have a mean above four of the five, which is the clearest demonstration there is that an average can sit where nobody lives. Six days of deliveries have a median of twelve and a half, a number that appears nowhere in the list, because with an even count the middle is shared by two values. A five-day sales list has a mode of 100 and a range of 50, and among the wrong answers are its own median and its own largest value, both true statistics of the same numbers and both answers to a different question.

Then probability, in pairs. Four blue chips and six red: draw twice with the first chip put back and the chance of two blues is four twenty-fifths; draw twice without putting it back and it is two fifteenths, because the second draw happens in a bag that the first one changed. The two questions use the same bag and the same wording up to one clause, which is where the whole difference lives. Alongside them, a straightforward draw, and the probability that something does not happen — countable either by counting what is left or by subtracting from one.

The set closes on what numbers cannot do. A website poll where forty of fifty voters chose blue supports a claim about fifty self-selected people and no claim at all about the population; the arithmetic in it is perfectly correct, which is what makes it worth examining. And six months of rising sales with one month down show a trend, no cause, and no forecast.

Everything is in plain words and digits. Each answer was worked twice, and an independent solver reproduced all twelve.

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• Calculate the mean of a list and say what happens to it when a value is added
• Find the median of a list with an even number of values, where the answer is not in the list
• Identify the mode and the range, and tell them from the median and the largest value
• Explain why an outlier makes the mean a poor description of a set
• Work out a probability from a described collection, and the probability that an event does not happen
• Tell a draw with replacement from one without, and calculate both
• Scale a proportion found in a sample to a larger population
• Say what a trend does and does not establish, and why a self-selected sample supports no general claim

Written for this exercise; every data set is a list inside its own question, with no charts. From the bank: "A group of five employees earns the following hourly wages: 15, 15, 18, 20, 100. Why is the mean a misleading measure of central tendency for this data?" The mean of that list is 33.6 — higher than four of the five wages actually paid.