Math for Journalists: Summary of Chapters 1-4 of ‘Math Tools for Journalists’
APRIL 22, 2011
In order to ensure accuracy, journalists sometimes have to use statistics, percentages and data. These include numbers — and numbers can scare writers who are so used to using words. But numbers are important in many stories. They help explain to readers. They help readers understand the issue or event or concept.
Numbers are precise, said Kathleen Woodruff Wickham, the author of this book. They also help to put issues into perspective.
- Percent increase/decrease: Percentage increase/decrease = (new figure – old figure) ÷ old figure
Convert to a percentage by moving the decimal two places to the right.
- Percent of the whole: Percentage of a whole = subgroup ÷ whole group
Move the decimal point two points to the right.
- Percent points: Distinguish between percent and percentage point. One percent is one one-hundredth of something.
- Convert fractions to percentages: convert a fraction to a decimal by completing division, to convert a decimal to a percentage move the decimal point two points to the right
13/15 = 13 ÷ 15 = 0.87
- Simple/annual interest: Percentages are often used to compute interest. The amount of money borrowed is called principal. Money paid for the use of money is called interest. The rate is the percent charged for the use of money. Amount of interest charged depends on the length of time borrowed money is kept.
Simple/annual interest formula: Interest = principal x rate (as a decimal) x time (in years)
- Payments on loans: consumers usually make monthly payments on loans for home mortgages or cars. The term of the loan is how long the borrower has to repay a loan. The monthly payment and total interest paid can be calculated.
A = monthly payment
B = original loan amount
R = interest rate, expressed as a decimal and divided by 12
N = total number of months
A = [P x (1 + R)^N x R] ÷ [(1 + R)^N – 1]
More information: The ^N in the air beside brackets is to the power of, so multiply the result of the brackets by itself N
number of times.
- Interest on savings: savings accounts and certificates of deposit generally pay compound interest
B = balance after one year
P = principal
R = interest rate
T = number of times per year interest is compounded
B = P(1 + [R ÷ T])^T
- Salary increase: Original salary x percent increase = dollar amount of salary increase for first year
Original salary + salary increase = salary for first year of contract
First year salary x percent increase = dollar amount of salary increase for second year
First year salary + salary increase = salary for second year
- Percentile: a percentile is a number representing the percentage of scores that fall at or below the designated score. It is based on the relationship to all other scores. If a test-taker scored in the 65th percentile then 65 percent of the people who took the test scored the same or lower.
Percentile rank = (Number of people at or below an individual score) ÷ (number of test takers)
Or turn the formula around to find out the number of people who scored at or below a certain point.
Number of people scored at or below that level = (Percentile) x (number of test takers)
- Standard deviation: standard deviation is a figure that indicates how much a group of figures varies from the norm. A small standard deviation means the figures are consistently grouped around the mean. A high standard deviation can mean there are inconsistent results. Standard deviation is shown as data in a bell curve. It can be used as a unit of measure along the bell curve. The middle of the curve (the highest point) is the mean and the rest spreads out on either side. The steeper the bell curve the smaller the standard deviation (since more numbers are close to the mean). A more spread out bell curve represents a large standard deviation. Data can exhibit a typical distribution where 68 percent of the scores will fall within one standard deviation (either positive or negative), 95 percent will fall within two standard deviations and 99 percent will fall within three standard deviations.
Subtract the mean from each score in the distribution.
Square the resulting number for each score.
Compute the mean for these numbers. This figure is called variance.
Find the square root of variance.
- There are many federal statistics that can be important for journalists to know how to find and generate.
- Unemployment: every month the U.S. Department of Labor, Bureau of Labor Statistics (BLS) issues a report on U.S. employment. The employment rate is defined as the percentage of the labor force that is unemployed and actively seeking work. Labor force means anyone over the age of 16 who has a job or has looked for one in the past four weeks (except unemployed people who aren’t actively seeking work and people who are institutionalized, such as in prison). Being employed means the person did some work for pay in the week before the survey was taken or did at least 15 hours of unpaid work for a family enterprise. A group of 60,000 households is interviewed, called the Current Population Survey. This data creates the unemployment figures for each state and the nation. BLS adjusts some statistics to take into account seasonal employment changes. Visit www.bls.gov.
Unemployment rate = (unemployed ÷ labor force) x 100
- Inflation and Consumer Price Index: inflation continuously affects the economy. U.S. inflation is measured by the CPI, which is a figure determined by the BLS. It shows the amount of inflation in any given month for eight major product groups (food and beverages, housing, apparel, transportation and recreation). CPI data are collected from 23,000 retail and service businesses each month. Information on rents is collected from about 50,000 landlords and tenants. CPI is reported in several ways. Sometimes it’s written as an index number (some number more than 100, shows how much prices have increased since the base CPI 100 was created in 1984). Or the change in CPI is reported as a monthly or annual inflation rate.
Monthly Inflation Rate = (Current CPI – Prior Month CPI) ÷ Prior Month CPI x 100
- Annual inflation rate: Compare the current CPI with CPI of that month in a previous year.
A = Annual Inflation Rate
B = Current month CPI
C = CPI from same month in previous year
A = (B – C) ÷ C x 100
- Adjusting for inflation: a historical figure is changed to represent how large it would be in current dollars. BLS has an inflation calculator on its website.
A = Target year value, in dollars
B = Starting year value, in dollars
AC = Target year CPI
BC = Starting year CPI
A = (B ÷ BC) x AC
- Future prices: If you want to figure out how much something will cost a year from now, you can with the current rate of increase of the CPI, if the rate will remain the same. Find the annual interest rate and apply it to the original price and compound it.
C = Cost after one year
K = Original cost
I = Inflation rate
C = K(1 + [I ÷ 12])^12
- Gross Domestic Product: GDP is the value of goods and services produced by a nation’s economy. It can gauge the direction of the country’s economy. When GDP increases, the economy is considered healthy and if it is decreasing the economy may be in a recession. The change in GDP is watched (rather than its level). GDP is often converted into “real” GDP, which holds prices of the measured items consistent to the prices they were in 1996. Real GDP shows changes in quantities of goods and services produced. GDP is reported quarterly and the rate of GDP growth is reported annually.
C = Consumer spending on goods and services
I = Investment spending
G = Government spending
NX = Net exports (exports minus imports)
GDP = C + I + G +NX
- Trade balance: Trade balance is the difference between goods and services a country exports and imports. For the U.S. the trade balance has been a negative number for years, meaning that Americans are importing more goods than exporting. There are seven major categories for exports and imports (capital goods other than autos; services including travel, royalties and license fees and other private services; industrial supplies; autos and auto parts; consumer goods; food and beverages and other).
Trade balance = Exports – imports
It’s important for journalists to have math skills, to at least understand what the formulas are doing. Journalists are communicating information and data to the public, so they must understand what they are communicating.
1. Percent decrease:
Bill Gates is decreasing his donations to charity from $735,460 to $356,789. By what percentage is the donation cut?
$356,789 – $735,460 = -$378,671
-$378,671 ÷ $735,460 = -0.5148
So the donation was cut -51.5 percent.
2. Percentage of a whole:
The concession stand at the local movie theatre makes $25,000 a year. The entire movie theatre makes $899,897. What percentage of the entire earnings does the concession stand produce?
$25,000 ÷ $899,897 = 0.0277
So the concession stand produces 2.7 percent of the whole movie theatre earnings.
Delilah Vale received an overall score of 78 on his ACT test. 4,683 other students took the test. Vale’s score is equal to or higher than the scores of 1,754 other students. What is Vale’s percentile rank?
1,754 ÷ 4,683 = 0.3745
Vale’s percentile rank is the 37th percentile.
4. Simple/annual interest:
George Fink borrowed $4,530 from the Risky LenderBank to make a down payment on an apartment. He agreed to pay 8 percent interest, payable in one payment at the end of three years. What is George’s interest payment?
$4,530 x .08 x 3 years = $1,087.2
So his interest payment is $1,087.2.