Journalists need math tools too, part two

7. Stocks and Bonds

Business raise money using stocks and bonds, so any reporter covering business should be familiar with them. When an investor buys stocks of a company, they become a part owner of a small portion of the company. The price of a stock changes depending on the demand at the time. Wickham lists these typical sections of a stock published in a newspaper:

  • 52-week High/Low (high and low prices)
  • Stock (symbol/name of stock)
  • Div (most recent annual dividend)
  • PE (stock price divided by per-share earnings
  • Last (price of share at end of previous day)
  • Change (change of stock price that day)

Bonds are essentially loans from an investor and corporations and governments use them to raise money. Unlike stocks, bonds are a low-risk investment and earn a set interest. The face value is the amount of money the owner will receive when it is mature. However, companies sometimes sell bonds before they are mature, so to calculate the current yield, Wickham offers this formula:

Current yield = (interest rate x face value) ÷ price

To calculate bond costs:

Bond cost (interest) = amount x rate x years

Indexes, such as the Dow Jones Industrial Average keep track of the price of certain stocks in order to provide an overview for investors.

Example problem:

John Smith paid $1500 for a bond with a $2000 face value and a 3 percent interest rate. What is the bond’s current yield?

Answer:

(3% x $2000) ÷ $1500 = 4%

8. Property Taxes

Property taxes are the biggest income for local governments and they help pay for running expenses. For example, a city decides how much money they need and then they divide that number among property owners. Property taxes are measured in mills, which is 1/10 of a cent and Wickham says they are “expressed in terms of mills levied for each dollar of assessed valuation of property. Remember that the assessed and actual value can be different. Formula for mill levy:

Mill levy = Taxes to be collected by the government body ÷ assessed valuation of all property in the taxing district

The appraisal value of a property can depend on:

  • Location
  • Living area
  • Stories
  • Exterior wall type
  • Age
  • Construction quality
  • Amenities

Assessed value formula:

Assessed value = Appraisal value x rate

Tax formula

Tax owed = Tax rate x (assessed value of the property ÷ $100) (if based on amount per $100 of assessed value)

Example problem:

What is the assessed value of a house appraised at $157.000 with a 25% appraisal value?

Answer:

$157.000 x 0.25 = $39.250

9. Directional Measurements

News stories often deal with directional measurements. They can provide more insight about people’s action and answer questions that readers may have. Being able to check these figures will lead to more accurate stories for your audience.

Formulas for distance, rate and time provided by Wickham:

Distance = rate x time

Rate = distance ÷ time

Time = distance ÷ rate

The difference between speed and velocity is that the latter indicates direction while the former doesn’t. The speed something is currently traveling when you take a snapshot of the moment is the instantaneous speed. Reporters are usually more interested in the average speech. To calculate acceleration, use this formula:

Acceleration = (ending velocity – starting velocity) ÷ time

Using the acceleration, you can find the speed at which a falling object hits the ground on earth.

Ending speed = 2(acceleration x distance)

Wickham defines momentum as the “force necessary to stop an object from moving. This is the formula:

Momentum = mass x velocity

Example problem:

The new Tesla Roadster can reach 60mph in 1.9 seconds. What is its rate of acceleration?

Answer:

(60mph – 0mph) ÷ 1.9s = 31.6 mph/s

10. Area measurements

Knowing how to express measurements can help with clarity in your stories. Often, analogies are useful for creating context and can help readers visualize measurements more easily. However, this only works when the reader understands the comparison and is also ineffective when exact numbers are needed (like number of parking lots).

These are formulas Wickham provides to different area measurements:

Perimeter = (2 x length) + (2 x width)

Area rectangle = length x width

Area triangle = ½ base x height

Area circle = π x radius²

Circumference = 2π x radius

Example problem:

A new parking lot is 200m wide and 300m long. What is the perimeter?

Answer:

(2 x 200m) + (2 x 300m) = 1km

11. Volume Measurements

Volume measurements play an important role when reporting about goods and provide additional context for articles. Wickham provides some common liquid measurements:

2 tablespoons = 1 fluid ounce

½ pint = 8 ounces

2 quarts = ½ gallon

1 U.S. barrel = 31.5 gallons

Volume of a rectangular solid:

Volume = length x width x height

The measurement for firewood is a cord. One cord equals 128 cubic feet when the wood is stacked in a line or row.

There are three different types of tons. They can be converted using the following table:

  • Short ton to long ton: Multiply by .89
  • Short to metric ton: Multiply by .9
  • Long to short ton: Multiply by 1.12
  • Long to metric ton: Multiply by 1.02
  • Metric to short ton: Multiply by 1.1
  • Metric to long ton: Multiply by .98

Example problem:

How many servings are there in 1 liter of orange juice?

Answer:

1L = 1000ml

One serving is 237ml

1000ml ÷ 237ml = 4.2

There are 4 servings.

12. The Metric System

The metric system is based on multiples of ten and is used in most places around the world. Journalists should know both metric and imperial to appeal to a wider audience and be able to interpret data, regardless in what form it is written. Wickham lists the prefixes and numerical values for the metric system:

  • micro 0.000001
  • milli 0.001
  • centi 0.01
  • deci 0.1
  • 1.0
  • deka 10
  • hecto 100
  • kilo 1,000
  • mega 1,000,000
  • giga 1,000,000,000
  • tera 1,000,000,000,000

Although Wickham provides conversion rates for most units, it is most practical to simply look it up when needed or to practice using the metric system to get a sense for the units, thus not needing to convert it in the first place. However, it is useful to keep these style rules in mind:

  • The unit names are lower case except for degrees Celsius.
  • Unit symbols are also lower case except for liters and names derived from people.
  • Prefixes for a million or more are capitalized and vice versa.

Example problem:

You are studying abroad in Denmark and the room you are in feels too cold. There is no thermostat because climate control is not used in most European countries, but there is a temperature sensor hanging on the wall. What value is it likely indicating?

Answer:

19°C or lower.