Browsing category statistics

The Classwiz and the Normal Distribution

I realised today I’ve been advising my students… not wrong, exactly, but imprecisely. Capriciously. Unmathematically. Even through it was in statistics, where such things are usually tolerated, I felt it was worth putting it right. It was in a scenario such as this: The times an athlete takes to run

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Middle children

At an academic conference; 22 people in the room. Speaker asks who is a middle child. There is only one in the entire group - him. Striking (if anecdotal) confirmation of stereotypes about birth order. — Leigh Caldwell (@leighblue) December 14, 2018 As a loyal listener to More or Less,

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Random number tables

I challenge you to write an interesting blog post about random number tables — Jo Morgan (@mathsjem) June 28, 2017 If you flick to the back of an old A-level formula sheets, you might spot a list of random digits like this one from an MEI book: Why on earth

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The Mathematical Ninja and the Poisson Distribution

"What are the ch..." "About 11.7%," said the Mathematical Ninja. "Assuming $X$ is drawn from a Poisson distribution with a mean of 9 and we want the probability that $X=7$." "That's a fair assumption, sensei," pointed out the student, "given that that's what the sodding question says." A wiser student

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How do you estimate the normal distribution for large $z$?

In working out a recent blog post, I had cause to find the probability, in a standard normal distribution, of $z < -23$. Beyond "that's a REALLY SMALL NUMBER"1, I was stumped. Could I get anywhere close mentally? A good question. Starting from the definition of the normal distribution, $p(z)

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Ask Uncle Colin: A Stretch, Indeed

Dear Uncle Colin, My research has determined that female adults have a mean overhead reach of 208.5cm, with a standard deviation of 8.6cm, and follows a normal distribution. I wanted to know the probability that the mean overhead reach of 50 female adults would lie between 180cm and 200cm and

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The Echo and a simple answer

Don't get me wrong, The Dorset Echo is one of my favourite local newspapers. They have been kind enough to feed my ego on several occasions, and even if their headlines sometimes don't quite reflect the gist of the story, I appreciate that. This time, though, they've gone too far.1

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Picking a station

There's a lot of dead time to fill up when you're covering the Boat Race. Once you've interviewed one gaggle of inebriated revellers from each of the two universities, you've interviewed them all. Once you've explained that the best strategy is to go faster than the other boat, there's not

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Poissons and binomials

A student asked: What's the link between the Poisson formula and the binomial? ... and I started to cry a little bit. Infinitely many trials You use the Poisson distribution when you have events happening at a constant rate, on a continuous time-frame - as opposed to the binomial, which

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Why the Mathematical Ninja hopes for a hard exam

The Mathematical Ninja sighs. "Say that again?" "I hope it's an easy paper!" says the student, brightly. Wearily, the Mathematical Ninja goes to the board and sketches two curves. They look a little like boa constrictors that have swallowed elephants. "You're above average, correct?" he asks. The student doesn't look

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