Numeracy for Journalists

I. Numeracy for Journalists: Percent, percent change, rate, median, mean, normalization

Percent

Pizza Hut overwhelming contributed to Republicans

number / total number x 100 = percent

A percent is part of one hundred, or part of a whole. Percents describe relationships between two numbers that, when used literally, might lack context or be hard to understand. To write, “Jane Brown received 7,542 votes out of a total of 12,165” may be accurate, but the relationship between the numbers is more clear and meaningful when the percent tool is used: “Jane Brown received 62 percent of the vote.”

Percent of total can show you patterns or disparities in sets of numbers. For example, if you have a data set that tells you that state employees got a total of $3.5 million in raises this year, and you know the governor’s salary for this year and for last year, you can figure out what percent of the total in raises given out went to the governor. You can then compare that with the percent of total that was awarded in raises to, say, clerks at the unemployment office. Thus, by calculating percent of total for a category of numbers, such as salaries, you will identify each employee’s or each department’s share of the budget “pie.” In fact, a pie chart can help you analyze these data or illustrate your news report.

Percent Change

To calculate the percent change:

new number – original number / original number × 100 = percent change

1) (New – old) / old = decimal value
2) Decimal value x 100 = percent change

If your answer is a negative number then this is a percentage decrease.

Rate

total events / total population x “per” value = rate

For the “per” value, choose a round number like 100 or 1,000 or 100,000 or even 1 million, depending on the size of the population. — Poynter U: Math for Journalists

Rate is a very handy math tool when you want to make a comparison between quantities of two things that are not alike. Let’s take an example: murder rates in U.S. cities in a given year. What do we need to know to apply the rate tool to this sort of data? Since murders happen to people, we’ll need to obtain (1) city population in that year and, (2) number of murders in that city in that year. Most data about homicide is published as the rate per 100,000 residents, which allows us to make meaningful comparisons. “Per capita” is Latin, “for each head.”

2018

Normalization vs. Absolute numbers examples

Crime in the subway

“The difference between the total and the per–100,000 number is important not just because it changes the picture. It’s the much more interesting number. The total number of crimes means nothing for the individual. What is much more relevant is how many crimes happen per person, because that provides a much closer estimate of each individual’s risk of becoming a victim. Number 2, 125th St, has over six times the rate per 100,000, and number 5, Broadway Junction, has almost ten times the rate (but less than half the total number) compared to Times Square.”

— “Putting Data into Context”

NYTimes COVID-19 Data

Adjusting for inflation

Generally, if dollar values differ over time by three years or more, a cost-of-living adjustment should be calculated to ensure inflation has been accounted for and the comparisons being made are fair. Change in cost of living adds incredibly useful and accurate depth to news reports.

You can use an automatic Web calculator to adjust for inflation. Just plug in the dollar amount ($1) and the year (1913) and poof, your answer — what that dollar was worth in 2012 — shows up on the screen. There are a few calculators on the Bureau of Labor Statistics website. If you plug in the $1 and enter 1913 as your starting point, the calculator will tell you that the 1913 dollar was worth $23.19 in 2012.

— Poynter U: Math for Journalists

Ratio

Ratio is a way of explaining how two similar things relate. Ratios crop up in daily life all the time — in recipes, measurements — and in journalism in stories on elections, sports, education, health and much more. For instance, in a city council race, Candidate Brown got 75,347 votes and Candidate Smith only got 24,994, you could accurately tell your audience that Candidate Brown won by a ratio of 3-to-1. That means that, for every vote that Smith got, Brown got 3 votes.

Order is important in expressing a ratio. If you were in a class that had 5 men and 15 women, you could say that the ratio of men to women was 5-to-15. Or that the ratio of women to men was 15-to-5 or reduce it to 3-to-1. But it’s crucial to keep the objects you are counting or measuring in the correct order.

Ratios are easily confused with fractions and percents, but the numbers mean very different things. For example, if candidate A won an election by a 5:4 margin, that does not mean that candidate A got 4 out of 5 votes. It means that for every 4 votes that candidate B got, candidate A received 5. So, candidate A got 5 out of every 9 votes, or about 55 percent. — Poynter U: Math for Journalists

Distribution — Robert Niles “Stats Guide”

A normal distribution of data means that most of the examples in a set of data are close to the “average,” while relatively few examples tend to one extreme or the other. Let’s say you are writing a story about nutrition. You need to look at people’s typical daily calorie consumption. Like most data, the numbers for people’s typical consumption probably will turn out to be normally distributed. That is, for most people, their consumption will be close to the mean, while fewer people eat a lot more or a lot less than the mean.

Standard Deviation — Robert Niles “Stats Guide”

If you are comparing test scores for different schools, the standard deviation will tell you how diverse the test scores are for each school. Let’s say Springfield Elementary has a higher mean test score than Shelbyville Elementary. Your first reaction might be to say that the kids at Springfield are smarter. But a bigger standard deviation for one school tells you that there are relatively more kids at that school scoring toward one extreme or the other. By asking a few follow-up questions you might find that, say, Springfield’s mean was skewed up because the school district sends all of the gifted education kids to Springfield. Or that Shelbyville’s scores were dragged down because students who recently have been “mainstreamed” from special education classes have all been sent to Shelbyville.

Margin of Error Robert Niles “Stats Guide”

The margin of error in a sample = 1 divided by the square root of the number of people in the sample.

You’ve probably heard that term — “margin of error” — a lot before. Reporters throw it around like a hot potato — like if they linger with it too long (say, by trying to explain what it means), they’ll just get burned. That’s because many reporters have no idea what a “margin of error” really represents.

If a poll has a margin of error of 2.5 percent, that means that if you ran that poll 100 times — asking a different sample of people each time — the overall percentage of people who responded the same way would remain within 2.5 percent of your original result in at least 95 of those 100 polls.

Operations Order