Math for journalists
For more information on how to successfully use numbers in news stories, consult: John Allen Paulos, "Innumeracy," Vintage Books, 1988 John Allen Paulos, "A Mathematician Reads the Newspapers," Basic Books, 1995 Victor Cohn, "News and Numbers," Iowa State University Press, 1989 Philip Meyer, "The New Precision Journalism," Indiana university Press, 1991
Before you can use a spreadsheet, you need to understand the math behind the program. Here is one reporter's instructions, as presented at the 1996 IRE National Conference in Providence, R.I. Excel uses cell addresses to instantly perform the calculations below, so once you understand the math, you can make a spreadsheet do the heavy lifting.
The Great Flood: Did it happen?
It's simple arithmetic, and context, that will save your butt, not complex statistical analysis or calculus. We'll cover percent, percent change, percentiles, compound percentages, mean vs. median, context, and resources. The Bible says, "All high hills that were under the whole heaven were covered." Let's assume the highest peak was around 5,000 feet. Rain: 40 days + 40 nights = 960 hours. Rate: Two to three inches per hour is considered heavy rain. So, let's assume one foot per hour. Amount: 960 feet, not accounting for any runoff. How hard would it have had to rain? 5,000 feet / 960 hours = 5.21 feet per hour, not accounting for any runoff.
Percents
Percents are a standardized way of expressing a fraction, where the denominator (the bottom number) equals 100. So, 1/4 is 25 percent, 1/3 is 33 percent, etc. Percent Change = "change"/"old" Example: 1996 budget = $500,000 1997 budget = $400,000 Change = $100,000 Percent change = $100,000 / $500,000 0.2 = minus 20 percent. (We frequently say something declined by 20 percent.) Note that if the budget were cut by $100,000 this year and restored next year, that would be a 20 percent decrease, followed by a 25 percent increase. Lesson: You can't just add percentages to compute an overall percentage change. In general, quantities cannot decline by more than 100 percent, because there's nothing left.
However, there is no upper limit on how much something can increase, in percentage terms. Example: Michael Jordan's 1986 salary = $1 million Michael Jordan's 1996 salary = $8 million Change = $7 million Percent change: $7,000,000/$1,000,000 = 7 = 700 percent
Percentage points
These are useful when comparing two numbers already expressed as percentages. March unemployment = 5 percent April unemployment = 6 percent Change = 1 percentage point Percent change = 1 (the change) / 5 (the old) = 20 percent
Compound percentages
A school district signs a contract giving teachers 8 percent raises in each of the next three years. What's the percentage increase in the contract? Note that the percent increase is applied to a bigger base each year. Assume the average teacher made $30,000 under the old contract. First year: $30,000 * 0.08 = $2,400, so new salary is $32,400. Second year: $32,400 * 0.08 = $2,592, so new salary is $34,992. Third year: $34,992 * 0.08 = $2,799, so new salary is $37,791. Total percent change: $37,991 - $30,000 = $7,991 (change)/$30,000 (old) = 0.2597 = 25.97 percent
Mean vs. median
Mean is an arithmetic average. Add up the values and divide by the number of values. Median is the middle value in a group, where the values have been ranked from top to bottom. (If there are an even number of members in the group, the median is the average of the middle two.) How they can differ: Assume there are 100 workers at a company, and 95 make $30,000 a year, while five make $300,000. Mean = (95 * 30,000) + (5 * 300,000))/100 = $4,350,000/100 = $43,500 Median = $30,000 (the average of the 50th and 51st highest salaries) Which is more reflective?