Math cribsheet

From Reporting Cookbook: www.forjournalists.com/cookbook

[edit] Introduction

It's a common newsroom joke: "I got into journalism so I wouldn't have to do math." Yet we all wind up having to do it -- calculating a percentage increase on a school system budget, for example.

This newsroom math crib sheet was originally created by Steve Doig, an Arizona State University professor who graciously granted permission to redistribute and modify it. People looking for more help should check out Sarah Cohen's "Numbers in the Newsroom: Using Math and Statistics in News" book. It's great to have on the bookshelf, and nicely priced.

All that said, you wouldn't be reading this if you didn't think you needed help soon.

[edit] Converting a fraction into a decimal

Divide the top number by the bottom number.

5/8 = 0.625

17/64 = 0.265…

[edit] To convert a decimal into a percentage

Multiply by 100 (or simply move the decimal two places to the RIGHT)

0.658 = 65.8%

1.255 = 125.5%

[edit] To turn a percentage into a decimal

Divide by 100 (or simply move the decimal two places to the LEFT)

43.7% = 0.437

148.2% = 1.482

[edit] To get X% of Y:

Turn X% into a decimal, then multiply it by Y

20% of 90 = 0.20 * 90 = 18

130.5% of 45 = 1.305 * 45 = 58.7…

[edit] To compare X and Y using percentages (X is what percent of Y?)

X is (X/Y * 100) percent of Y

5 and 8: 5/8 = .625 = 62.5%, so 5 is 62.5% of 8

8 and 5: 8/5 = 1.6 = 160%, so 8 is 160% of 5

[edit] To compare X and Y using percentage differences

X is ((X/Y –1) * 100) MORE/LESS than Y

Use MORE THAN if the answer is positive, and LESS THAN if it’s negative

5 and 8: 5/8 –1 = .625 – 1 = -0.375 = -37.5%, so 5 is 37.5% less than 8

8 and 5: 8/5 –1 = 1.6 – 1 = .6 = 60%, so 8 is 60% more than 5

[edit] To compare a NEW number with an OLD number using percentage change

NEW has increased/decreased ((NEW/OLD –1) * 100) percent since OLD

Use INCREASED if the answer is positive, and DECREASED if it’s negative

This year’s $8 million budget is a 60% increase over last year’s $5 million budget.

This year’s $5 million budget is a 37.5% decrease from last year’s $8 million budget.

[edit] To calculate rates (the number of events per some standard unit)

Do this to account for different size populations. RATE = (EVENTS / POPULATION) * (“PER” Unit)

Problem: If there were 320 murders in a population of 1,937,086, what is the murder rate per 100,000?

First, divide the 320 murders by 1937086 = 0.0001652…

Now multiply 0.0001652… by 100,000 = 16.5 murders per 100,000 population

[edit] To calculate the effect of inflation using the Consumer Price Index (CPI)

With this formula, all you need is any three of the numbers to calculate the fourth.

CPI now = 188; CPI in 1965 was 31; price of gas in 1965 was $0.30 per gallon.

X / 0.30 =188 / 31

X = (188 / 31) * 0.30 = 6.06 * 0.30 = $1.82 per gallon (cost of 1965 gas in today’s dollars)

[edit] To estimate the size of a crowd

Get the size of the area in square feet (two paces is approximately your height) Divide the square footage by 10 for a loose crowd, or 7 for a tight crowd.

[edit] Newsroom statistics

Mean (average): Add the numbers, then divide by how many numbers there are: 1+2+9+15/4 = 7

Median: Sort the numbers in order, then find the middle value: 1, 2, 9, 15: 5.5 (no middle value, so use average of closest numbers, 2 and 9, for 2+9/2)

Sampling error margin: 1/√N (example: sample of 625: 1/√625 = 1/25 = 0.04 = +/- 4 points)