Earlier today I set these three puzzles about deception. Here they are again with solutions.

1. Super syllabus

A school cohort has two classes. At the end of the year 1, all pupils are graded. When all the pupils are listed in grade order, the median pupil is a C.

(The median is the middle value in a data set listed from smallest to largest.)

For year 2, the school introduces a new syllabus. At the end of the year, all pupils are again graded. Now when the pupils are listed in grade order, the median has dropped to a D.

Devise a scenario in which the new syllabus in fact improved every pupil’s grade.

Solution

Imagine that in the first year everyone in one class gets a C and everyone in the other gets has an E. If there is one more person in the first class, the median pupil gets a C.

Now lets say that in the second year, everyone with a C improves to a B, and everyone with an E improves to a D. All it takes is for two new pupils to join the second class and score a D or below for the median of the cohort to drop to D.

Yes, you might complain that I didn’t make clear that new pupils could join. But that’s the point! Often statistics deceive us because there are gaps in our knowledge.

2. Peculiar poll

Two market research companies, Smith Surveys and Jones Polls, each conduct a poll on support for a government policy.

Both polls of 125 people show that the policy is more popular amongst men.

READ THE DATA BELOW TO CHECK THAT THE PREVIOUS SENTENCE IS CORRECT.

Is the policy more popular amongst men or amongst women?

Data from Smith Surveys. Men who support the policy: 21/25, or 84 per cent. Women who support the policy: 80/100, or 80 per cent.

Data from Jones Polls: Men who support the policy: 22/100, or 22 per cent. Women who support the policy: 5/25, or 20 per cent.

Solution

You would expect it to be the case that if both polls show that the policy is more popular amongst men, then the policy is more popular among men.

But this is not true! Do the sums:

Men who support the policy overall: 43/125 = 34 per cent

Women who support the policy overall: 85/125 = 68 per cent

The policy is more popular among women.

This statistical curiosity is called Simpson’s Paradox, the phenomenon that trends in certain data sets can be reversed when the sets are combined.

Smith happened to survey mostly women in a place or way that produced high support overall, while Jones surveyed mostly men in a place or way that produced low support overall. When those different figures are combined the resulting figures point in the opposite direction.

3. Anguish Languish (prize draw!)

Anguish Languish is an ersatz language created by the US linguist Howard L Chase in which an English text is “translated” into a nonsense string of similar-sounding English words. (i.e English language = anguish languish.) Chase invented it to show “the marvelous versatility of a language in which almost anything can, if necessary, be made to mean something else.”

I asked readers to submit some examples to win a free copy of You Don’t Know What You’re M ss ng by Kit Yates.

The most popular subject was today’s news and we will miss a PM who if nothing else has a surprisingly homophone-friendly name.

Star myrrh scone

(Starmer’s gone.)

Good bike here, fair wheel.

(Good by Kier, farewell.)

Soak eerie mane sin faun, ow! Andes potent chili necks.

(So, Kier remains in for now. Andy’s potentially next.)

Goods peed KISSED Armour

(Godspeed Kier Starmer)

Other notable contributions were

Wench all wheat tree metre gain

(When shall we three meet again?)

Eats ahead nog knife, forest.

(It’s a hard knock life, for us.)

Lord Fig-Wit against tie-in

(Ludwig Wittgenstein)

Anna plaid hey key psst thud Octo hey whey!

(An apple a day keeps the doctor away._

But the winner is Edward Barrett for the nursery rhyme:

Myriad Al tell ’em, eats fleas worse wight ass know

(Mary had a little lamb, its fleece was white as snow.)

Thanks to everyone who submitted a line – I hope you had fun. I’ll be back in two weeks.

You Don’t Know What You’re M ss ng by Kit Yates is available to buy on the Guardian Bookshop for £22.50.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.