Solutions to Today’s Puzzles – and the Anguish Languish Contest Winner
I presented three puzzles centered on deception. Here they are again, accompanied by their solutions.
1. School Cohort Grades and Median Changes
A school cohort consists of two classes. At the end of the first year, all pupils receive grades. When pupils from both classes are listed in order of their grades, the median pupil’s grade is a C.
(The median is the middle value in a data set arranged from smallest to largest.)
In the second year, the school introduces a new syllabus. After the year ends, all pupils are graded again. This time, when the pupils are listed in grade order, the median grade has dropped to a D.
Devise a scenario in which the new syllabus actually improved every pupil’s grade despite the median dropping.
Consider this scenario: In the first year, everyone in one class receives a C, and everyone in the other class receives an E. If the first class has one more pupil than the second, the median pupil’s grade is C.
Now, in the second year, suppose everyone with a C improves to a B, and everyone with an E improves to a D. If two new pupils join the second class and score a D or below, the median of the entire cohort drops to D.
It is important to note that I did not explicitly state that new pupils could join. This omission illustrates how statistics can mislead when there are gaps in our knowledge.
2. Polling Data and Simpson’s Paradox
Two market research firms, Smith Surveys and Jones Polls, each conduct a poll on support for a government policy.
Both polls surveyed 125 people and indicate that the policy is more popular among men.
Review the data below to verify the previous statement:
Smith Surveys: Men supporting the policy: 21 out of 25 (84%). Women supporting the policy: 80 out of 100 (80%).
Jones Polls: Men supporting the policy: 22 out of 100 (22%). Women supporting the policy: 5 out of 25 (20%).
One might expect that if both polls show the policy is more popular among men, the overall support would also be higher among men.
However, this is not the case. Calculating the combined data:
Men supporting the policy overall: 43 out of 125 (34%). Women supporting the policy overall: 85 out of 125 (68%).
Thus, the policy is more popular among women overall.
This statistical anomaly is known as Simpson’s paradox, where trends observed in separate groups reverse when the groups are combined.
In this case, Smith Surveys happened to survey mostly women in a location or manner that yielded high support, while Jones Polls surveyed mostly men in a context with low support. When combined, these differing figures produce an overall trend opposite to the individual polls.
3. Anguish Languish (Prize Draw!)
Anguish Languish is a playful language created by the American linguist Howard L. Chase. It involves “translating” English texts into nonsense strings of similar-sounding English words. (For example, “English language” becomes “anguish languish.”) Chase developed it to demonstrate “the marvelous versatility of a language in which almost anything can, if necessary, be made to mean something else.”
I invited readers to submit examples of Anguish Languish to win a free copy of You Don’t Know What You’re M ss ng by Kit Yates.
The most popular theme was today’s news, and many submissions referenced a prime minister who, if nothing else, has a name rich in homophones.
Soak eerie mane sin faun, ow! Andes potent chili necks.
(So, Kier remains in for now. Andy’s potentially next.)
Other notable contributions included:
Wench all wheat tree metre gain
(When shall we three meet again?)
It’s a hard knock life, for us.
Anna plaid hey key psst thud Octo hey whey!
(An apple a day keeps the doctor away.)
The winner is Edward Barrett for his nursery rhyme submission:
Myriad Al tell ’em, eats fleas worse wight ass know
(Mary had a little lamb, its fleece was white as snow.)
Thank you to everyone who submitted lines—I hope you enjoyed the challenge. I will return with another puzzle in two weeks.
You Don’t Know What You’re M ss ng is available for purchase via Bookshop for £22.50.
I have been setting puzzles here on alternate Mondays since 2015 and am always seeking excellent puzzles. If you would like to suggest one, please email me.
