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Newspaper numbers

By David Shaw, 11 October 2017

Mathematicians can find patterns wherever there are numbers. In this activity, see if there’s a pattern in the numbers inside a newspaper!

You will need

• Newspaper
• Highlighter
• Pen
• Paper

What to do

Read through these instructions in full before starting the activity. Make a prediction about what you’re going to find.

1. Look at an article in the newspaper, and skim through until you find the first number.
2. Circle this number, and then repeat this procedure with the next article.
   We recommend you ignore years and phone numbers, because they will skew the data.
3. If you don’t find a number, just move on to the next article.
4. Stop when you’ve circled about 20 numbers, or when you’ve run out of newspaper articles to look at.
5. Go back through and look at all the numbers you’ve circled. Count up the first digit of each number you’ve circled. For example, if you’ve circled $120 million, the first digit is 1.
6. Look at your tally. Are all the digits as common or are some more popular than others? Are you surprised with this outcome?

What’s happening?

When we did this activity, we found lots of numbers starting with 1, 2 and 3, and very few starting with 6, 7, 8 and 9.

This is a surprising phenomenon known as Benford’s law. It’s a bit tricky to explain, and there can be different causes depending on what type of number you’re looking at. But we can explore one example that might help.

Imagine you have a gold bar, worth $100. Every year, the value goes up by 10%. What happens to the first digit of the price? Let’s list the value each year:
$100, $110, $121, $133, $146, $161, $177, $195, $214, $236, $259, $285, $314, $345, $380, $418, $460, $505, $556, $612, $673, $740, $814, $895, $985, $1083 …

You’ll notice that far more of these prices start with a 1 than a 9. That’s because, if you start with 100 you need to increase it by 100% to get the first digit to change. In contrast, to change the first digit of 900, you only need to increase it by 12%

Benford’s law states that, when it applies, 30% of numbers will have a 1 as their first digit. That proportion steadily drops until you get less than 5% of numbers starting with a 9.

Benford’s law works for lots of numbers, but it doesn’t always work. It doesn’t work on phone numbers, or post codes, or page numbers. But it often works for prices, populations, and distances.

It can even be used to detect crimes, such as an accountant stealing money from a company and changing the numbers to hide their tracks. If a company’s accounts don’t fit Benford’s law, there might be something fishy going on!

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