How Numerous Are the Numerate?

14 Feb

I recently conducted a survey on Lucid and posed a short quiz to test basic numeracy:

  • A man writes a check for $100 when he has only $70.50 in the bank. By how much is he overdrawn? — $29.50, $170.50, $100, $30.50
  • Imagine that we roll a fair, six-sided die 1000 times. Out of 1000 rolls, how many times do you think the die would come up as an even number? — 500, 600, 167, 750
  • If the chance of getting a disease is 10 percent, how many people out of 1,000 would be expected to get the disease? — 100, 10, 1000, 500
  • In a sale, a shop is selling all items at half price. Before the sale, the sofa costs $300. How much will it cost on sale? — $150, $100, $200, $250
  • A second-hand car dealer is selling a car for $6,000. This is two-thirds of what it cost new. How much did the car cost new? — $9,000, $4,000, $12,000, $8,000
  • In the BIG BUCKS LOTTERY, the chances of winning a $10 prize are 1%. What is your best guess about how many people would win a $10 prize if 1000 people each buy a single ticket from BIG BUCKS? — 10, 1, 100, 50

I surveyed 800 adult Americans. Of the 800, only 674 respondents (about 84%) cleared the attention check—a question designed to test if the respondents were paying attention or not. I limit the analysis to these 674 respondents.

A caveat before the results. I do not adjust the scores for guessing.

Of these respondents, just about a third got all the answers correct. Another quarter got 5 out of 6 correct. Another 19% got 4 out of 6 right. The remaining 20% got 3 or fewer questions right. The table below enumerates the item-wise results.

ItemProportion Correct
Sofa Sale.97

The same numbers are plotted below.

p.s. You may be interested in reading this previous blog based on MTurk data.