50 Mathematical Ideas You Really Need to Know

the condensed idea Predicting how many ...

35 The normal curve The ‘normal’ curve plays a pivotal role in statistics. It has been called the equivalent of the straight lin ...

to work out the average distance of travel of the company’s staff. When Georgina drew a histogram of results the distribution sh ...

How the sample average is distributed The Central Limit Theorem is one reason why the normal curve is important to statisticians ...

This is called a binomial distribution of probabilities, which occurs where there are two possible outcomes (here a head or a ta ...

Distribution of the probability for the number of heads in 100 throws of a coin For large values of n, the variable x which meas ...

36 Connecting data How are two sets of data connected? Statisticians of a hundred years ago thought they had the answer. Correla ...

tendency to follow a straight line. It is positive because the straight line has a positive gradient – it is pointing in a north ...

could be a high correlation between house numbers and the combined ages of the house’s occupants but reading any significance in ...

data. Its value here is +0.6 which indicates a limited measure of agreement between Albert and Zac. If we treat the pairs of ran ...

5 feet 8¼ inches (173.4 cm) which value he called the mediocrity. He found that children of very tall mid-parents were generally ...

Let’s plot this on a graph, where we’ll make the x coordinate the number of customers (we call this the explanatory variable) wh ...

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37 Genetics Genetics is a branch of biology, so why is it in a mathematics book? The answer is that these two subjects cross-fer ...

A burning question in the field of biology arose at the beginning of the 19th century. Would brown eyes eventually take over and ...

The hybrid genotypes bB and Bb are identical so the probability of this occurring is 0.21 + 0.21 = 0.42. Expressed as percentage ...

respectively p + r = 0.4 and r + q = 0.6. So the distribution of next generation of genotypes is 16%, 48% and 36%. Successive pr ...

intriguing mathematical properties. the condensed idea Uncertainty in the gene pool ...

38 Groups Evariste Galois died in a duel aged 20, but left behind enough ideas to keep mathematicians busy for centuries. These ...

Can we set up a mirror so that an object looks the same in front of the mirror as in the mirror? The word MUM has mirror symmetr ...