Browsing category statistics 1

Ask Uncle Colin: why does the normal distribution stop at $z=\pm 4$?

Dear Uncle Colin, In Statistics, we were shown a picture of the standardised normal distribution curve, and the base stops at +4 and -4. Why is it not $\pm 5$, $\pm 10$, or anything else? Is there something special about 4? -- Got An Unanswered Statistics Struggle Dear GAUSS, The

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Conditional probability and the normal distribution

Until fairly recently, you could throw a handkerchief over the variety of normal distribution questions you might expect to see in an EdExcel S1 exam. It would be one or more of: given a mean and a standard deviation, work out the probability that the random variable is larger or

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How do I decide whether to take things away from 1 (Normal distribution)

A student asks: I'm never sure whether I have to take the number that comes out of the normal distribution table away from 1. How do you know? It's a familiar song: you've worked out your $z$-score (naturally, you remember that this means "how many standard deviations you are above

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Why are there so many equations for variance?

A student asks: Why are there so many equations for the variance? In S1, depending on the board you're working with, you might need to know three equations for variance. For listed data, it's: $\Var(X) = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2$ For grouped data, it's: $\Var(X) = \frac{\sum fx^2}{\sum f}

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Why are outliers defined like THAT?!

My own imagination asks: Why is an outlier defined as 1.5 interquartile ranges outside of each quartile? Great question, imagination! The simple answer, I think, is that it's a nice and easy thing to work out, and 1.5 interquartile ranges is quite a long way from the central box (if

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A student asks: Why does variance do THAT?

A student asks: The mark scheme says $Var(2 - 3X) = 9 Var(X)$. Where on earth does that come from? Great question, which I'm going to answer in two ways. Firstly, there's the instinctive reasoning; secondly, there's the maths behind it, just to make sure. Instinctively Well, instinctively, you'd think

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How to remember which way the skewness goes

OK, this is a quick and dirty trick of the sort that I love and the Mathematical Ninja hates. He doesn't have much time for stats at all, truth be told, least of all skewness. However, I've had several students struggle to remember 'which way is which' when it comes

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Linear Interpolation: There’s More Than One Way To Do It

If I had £35 every time a student said "I don't get linear interpolation," I'd have pretty much the same business model as I do right now. Everyone knows it's something to do with finding medians and quartiles, and something to do with the class width and... stuff. Some can

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Normal distribution – but fast! Secrets of the Mathematical Ninja

"A $z$-score of 1.4," said the student, reaching for his tables. "0.92," said the Mathematical Ninja, without skipping a beat. "0.9192," said the student, with a hint of annoyance. "How on earth..." "Oh, it's terribly simple," said the Mathematical Ninja. "It turns out, for smallish values of $z$, the normal

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The Bayesian umbrella

At a recent MathsJam, there was a puzzle. This is nothing out of the ordinary. It went something like: If an absent-minded professor takes his umbrella into a classroom, there's a probability of $\frac{1}{4}$ that he'll absent-mindedly leave it there. One day, he sets off with his umbrella, teaches in

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