Tag Archives: Math Tools for Journalists

Math Tools for Journalists Part 3

By Megan Wanner

Many journalists do not realize it, but time, rate and distance problems are just as relevant now as they were during middle school math class.  These numbers can give stories a whole new dimension of accuracy that readers appreciate when trying to fully grasp a situation such as a car accident where the driver of one car thought he had time to cross in front of another car.

It is important not to only rely on the numbers given to you as a reporter, but to calculate your own in order to provide greater accuracy for your audience.  This may take more time, but it’s more important to be accurate than timely.

The basic formula for time, rate and distance is the same; the equation is just reworked to obtain each number.  One of the most important things to remember with these problems is to keep the units of measurement the same and convert when necessary.

Formula

Distance = rate x time

Rate = distance / time

Time = distance / rate

Speed, velocity, acceleration and momentum are also important measurements to know how to calculate.  Speed measures how fast something is going.  Velocity measures how fast something is going and in what direction it is traveling.  Typically, reporters only need to calculate speed.

 While a speedometer will give you “instantaneous speed,” reporters find more usage in average speed, calculated by dividing the traveled distance by the time it took to travel the distance.  As average speed is another word for rate, it can be plugged into the rate equation.

Average speed = distance / time

Acceleration is the starting velocity subtracted from the ending velocity then divided by time.

Acceleration = (ending velocity – starting velocity) / time

The acceleration due to the force of gravity is 9.8 meters per second per second.  This acceleration is the same for all falling objects barring the force of friction.  When working with falling objects, you typically only know the distance it fell.  Determining the speed at which an object was traveling when it hit the ground requires a simple manipulation of the acceleration equation.

equation 1

 

 

All moving objects have momentum, the force needed to stop an object from moving.

Momentum = mass x velocity

As a journalist, there are two good ways to explain measurements to your reader.  The first is by analogy, the second with simple numbers.

Analogies are a good way to give your readers a visual of how big something is.  For example, if a large tree takes down a power line, it is much easier to describe to readers how large the tree is by comparing it to a building its size.

Simple numbers are used when exact accuracy is needed in a story.  For this it is important to be familiar with area, perimeter, square feet, square yards, circumference and radius to write stories about construction, real estate, etc.

Perimeter is simply the measurement around an object determined by adding the lengths of all the sides together.

Area is the measurement of the region inside an object.

Area of square and rectangle = length x width

Area of triangle = ½base x height

The radius of a circle is the distance from the middle of the circle to any edge of the circle.  You need to know the radius in order to calculate the circumference or distance around the circle. 

equation 2

 

 

Volume details can add important context and accuracy to articles.  The basic formula for volume is length multiplied by width multiplied by height. 

Although the metric system is disliked in America, it is actually useful and used for an assortment of measurements.  As it is based on multiples of 10, it is actually easier to use and convert than the English standard version we are used to as it is only a matter of multiplying or dividing by multiples of 10.

Basic Definitions:

Meter—basic unit for length

Gram—basic unit for mass

Newton—basic unit for force

Liter—basic unit for volume

Celcius—basic unit for temperature

Prefixes:

micro (1 millionth) 0.000001

milli (1 thousandth) 0.001

centi (1 hundredth) 0.01

deci (1 tenth) 0.1

no prefix 1.0

deka 10

hector 100

kilo 1,000

mega 1,000,000

giga 1,000,000,000

tera 1,000,000,000,000

Practice Problems:

A car is traveling at a constant speed of 70 miles per hour to its destination 200 miles away.  How long will it take the car to get there?

Time = distance / rate

Time = 200 / 70

Time = 2 hours and 51 minutes

The local park is building a rectangular swimming pool for its community.  The pool is 30 feet by 20 feet.  In order to stake out the area for the pool, the committee must know how much area the pool is going to take up.

Area = length x width

Area = 30 x 20

Area = 600 feet2

In order to build a sidewalk around the pool, the committee must know what the perimeter of the pool will be.

Perimeter = 2lengh + 2width

Perimeter = 2(30) + 2(20)

Perimeter = 100 feet

A box of bananas is 3 feet long, 2 feet wide and a foot deep.  What is the volume of the box?

Volume = length x width x height

Volume = 3 x 2 x 1

Volume = 6 feet3

A sidewalk is measured to be 40 meters long.  How many centimeters is this?

40 meters x 100 = 4,000 centimeters

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Math Tools For Journalists Part 2

By Megan Wanner

As reporters, we are exposed to many polls and surveys taken as a way to gage what the population is thinking about any number of issues or topics that arise.  It is the reporter’s job to assess the validity and accuracy of these polls and surveys in order to articulate that to their readers.

Polls “are an estimate of public opinion on a single topic or question.”  Random selection is an important factor in taking polls as this means everyone in the population being studied has a chance at being selected.  As researchers cannot survey a whole population, random selection helps their sample group to be as representative of the population as possible.

Margin of error is the “degree of accuracy of the research based on standard norms.”  A confidence level indicates how confident researchers are in their results or “the probability of obtaining a given result by chance.”.  As the margin of error increases, the confidence level increases.  Reporters should be sure to include both margins of error and confidence levels in stories in order to give readers the opportunity to review the results themselves.

One of the most widely known surveys in America is the U.S. Census.  The results obtained during the Census are used to generate congressional districts proportional to the population.

Trey surveyed 50 people about their reactions to President Obama’s first 100 days.  Out of the people polled, 87 percent replied favorably towards Obama.  The margin of error for a survey of 50 people at the 95 percent confidence level is 13.9 percent.  What is the range of favorable opinion towards Obama’s first 100 days?

(87 % + 13.9 % = 100.9%) (87% – 13.9% = 73.1%)

Between 73.1 percent and 100.9 percent.

Reporting a business beat typically includes the ability to not only report numbers, but calculate them as well in order to report on financial statements, assets, equity, gross margin, profit, liabilities and other financials. 

Profit and loss statements are different for every business, but essentially calculate the profit by subtracting expenses from income.  Expenses include “cost of goods sold” referring to “direct expenses a business incurs in making or buying its products” and “overhead” referring to “expenses not directly related to the product being made, including salaries of employees, rent, utilities, insurance, etc.”  “Gross margin” is the difference between the “cost of goods sold” and the selling price.

When comparing companies, it is useful to calculate each of their EBITDA “because it shows how much cash a company is earning without regard to items unrelated to current business.  EBITDA stands for “earnings before interest, taxes, depreciation and amortization.”

Analysts and business owners use ratios on a regular basis to assess financial situations of companies.  Among these ratios are current ratios, quick ratios, debt-to-asset ratios, debt-to-equity ratios, return on assets, return on equity and price-earnings ratios.

Todd owns a muffin shop where he pays $1.35 for each muffin and sells them for $1.75 each.  What is his gross margin?

Gross margin = Selling price – cost of goods sold

$.40 = $1.75 – $1.35

If Todd sells 150 muffins per day, what is his gross profit per day?

Gross margin x Number of items sold = Gross profit

$.40 x 150 = $60

In order to rent his shop, Todd pays $100 per month, overhead expense.  What is his net profit for a month?

Gross margin – Overhead = Net profit

($60 x 30 days) – $100 = $1700

Companies sell stocks and bonds in order to raise money.  People buy stocks as investments and become a small part owner of the company.  A bond is “a loan from an investor to the government or other organization selling the bond.”

Market indexes are used to track prices of groups of stocks allowing investment analysts to measure overall market conditions.  Two of the most popular indexes are the Dow Jones Industrial Average, “the total value of one share each of 30 select stocks divided by a figure called the divisor, and National Association of Securities Dealers Automated Quotations (NASDAQ), “an automated quotation system that reports on trading of domestic stocks and bonds not listed on the regular stock markets.”

Ted paid $1,500 for a $1,800 bond with an 8 percent interest rate.  What is his current yield?

(Interest rate x Face Value) / Price = Current Yield

(8% x $1,800) / $1,500 = 9.6 %

Property taxes are a large source of income that local governments, school districts and other community organizations use to pay for day-to-day expenses.  Property tax rates are determined by dividing the total amount of money the governing body needs among the property owners in the tax district.  They are measured in units called mills, which are each one-tenth of a cent.

Property taxes are applied to assessed valuations, a percentage of market value.  Reappraisals are key in updating real property values to reflect current market values.

Appraisal values are based on the property’s use, its characteristics, current market conditions determined by recent sales in the immediate area and visual inspection of the property.  The assessed value of a property is based on local policies including credits and other adjustments.

Residential property is assessed at 40 percent of the appraised value.  The house is appraised at $180,000.  What is the assessed value of the house?

Assessed Value = Appraisal Value x Rate

$72,000 = $180,000 x .40