An overview of Kathleen Wickham’s ‘Math Tools for Journalists,’ chapters 9–12

Chapter 9: directional measurements

Reporters shouldn’t simply rely on numbers provided by people involved in a story. Checking the numbers in time, rate and distance problems usually involves just some basic math.

In time, rate and distance problems, the basic formula is the same, but components are switched around depending on the solution needed.

Distance = rate * time

Rate = distance / time

Time = distance / rate

Speed and velocity are not the same measurement. Speed measures how fast something is going, while velocity indicates its direction.

The speedometer on a car gives the driver the speed at exactly one moment. This is called instantaneous speed. A more useful figure for a reporter is average speed, which is calculated by dividing the distance traveled by the time it took to get there.

Average speed = distance / time

Acceleration = (ending velocity – starting velocity) / time

Therefore:

Ending velocity = (acceleration * time) + starting velocity

Mass is a measure of amount. Weight is a measure of the force of gravity pulling an object. Mass is the same regardless of gravity.

To determine the speed of an object when it hits the ground. One needs to manipulate the equation for acceleration.

Ending speed = √2(acceleration * distance)

Momentum is the force necessary to stop and object from moving.

Momentum = mass * velocity

Practice problem

Janet Adamson is writing about the speed of a train, which commonly passes through Elrond University’s campus. The train’s acceleration at full throttle is .3 miles per hour per second. If the train is already moving 30 mph, and accelerating at full throttle for 3 minutes, how fast will it be going?

Chapter 10: area measurement

Knowing how to express measurements in an accurate and clear way is vital to good journalism. Analogies are a great way for illustrating measurements that may be otherwise meaningless, but analogies sometimes fail when exact measurements are essential.

Premature of a rectangle           

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

Area of a rectangle

Area = length * width

Area of a triangle

Area = .5 base * height

Small spaces are measured in square inches or square feet. Larger areas, such as parking lots, are measured in square feet, square yards or square rods.

144 inches = 1 square foot

9 square feet = 1 square yard

30 square yards = 1 square rod

160 square rods = 1 acre

1 acre = 43,560

640 = 1 square mile

The radius of a circle is the distance from any edge to the middle. Knowing the radius is key to finding the circumference, or the distance around. Knowing the radius is also necessary to find the area of a circle.

Circumference = 2Pi * radius

Area = Pi * radius2

Practice problem

Elrond University’s quidditch field is 120 yards long with two end zones of 5 yards each and a width of 75 yards. What is the field’s parameter and area?

Chapter 11: volume measurements

Volume measurements play a key role in many articles, especially on the business beat.

Rectangular solid

Volume = length * width * height

Common liquid conversion

2 tablespoons = 1 fluid ounce

½ pint = 8 ounces, or 1 cup

1 pint = 16 ounces, or two cups

2 pints (32 ounces) = 1 quart

2 quarts (64 ounces) = ½ gallon

4 quarts (128 ounces) = 1 gallon

1 U.S. standard barrel = 31.5 gallons

1 U.S. gallon = 4/5 Imperial gallon

British or Canadian barrel = 36 Imperial gallons

Cord

A cord is commonly used to measure firewood, and is defined as 128 cubic feet.

Ton           

There are three different types of tons. A short ton is 2000 pounds. The British ton is the long ton, which is 2240 pounds. There is also a third type of ton called the metric ton, equal to 1000 kilograms, or 2204.62 pounds.

Practice problem

A famous book of college reviews sent one of their workers to Elrond University to measure the size of a student dorm room. The rectangular room is 8 feet by 12 feet by 12 feet. How many cubic feet is the dorm room?

Chapter 12: the metric system

Outside the United States, most of the world uses the metric system for nearly every type of measurement. The unit names are meter (length), gram (mass) and liter (volume).

Length (metric) U.S.
1 millimeter [mm] 0.03937 in
1 centimeter [cm] 10 mm 0.3937 in
1 meter [m] 100 cm 1.0936 yd
1 kilometer [km] 1000 m 0.6214 mile
Area (metric) U.S.
1 sq cm [cm2] 100 mm2 0.1550 in2
1 sq m [m2] 10,000 cm2 1.1960 yd2
1 hectare [ha] 10,000 m2 2.4711 acres
1 sq km [km2] 100 ha 0.3861 mile2
Volume/ Capacity (metric) U.S.
1 cu cm [cm3] 0.0610 in3
1 cu decimeter [dm3] 1,000 cm3 0.0353 ft3
1 cu meter [m3] 1,000 dm3 1.3080 yd3
1 liter [l] 1 dm3 2.113 fluid pt
Mass (metric)   U.S.
1 milligram [mg] 0.0154 grain
1 gram [g] 1,000 mg 0.0353 oz
1 kilogram [kg] 1,000 g 2.2046 lb

Temperature

(1.8 * °C ) + 32 = °F

.56 * (°F – 32) = °C

Practice problem

 While studying abroad, Janet Adamson was asked to cook her host family dinner. She needs approximately 3 pounds of flower to bake dessert. Will a 1 kg bag be enough? Why or why not?

An overview of Kathleen Wickham’s ‘Math Tools for Journalists,’ chapters 5–8

Chapter 5: polls and surveys

It is a reporter’s job to help an audience understand the accuracy of polls and surveys. Polls are an estimate of public opinion on a single topic or question.

Polls are most frequently used in politics and based on the representative samples. Surveys are also based on representative samples, but include a multitude of questions. These are usually used in the social sciences.

Sampling

A valid sample is large enough to represent the population that is being considered. Pollsters usually Aim for at least 400 interviews to keep the margin of error within acceptable limits.

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Margin of error indicates the degree of accuracy of the research based on standard norms. Margin of error is expressed as a percentage and is based on the size of a randomly selected sample. Margin of error refers to a percentage of the actual polled number, not the percentage of the result.

Confidence level is the level or percentage at which researchers have confidence in the results of their research.

Adjusted figures are figures that are statistically manipulated to compensate for missing data.

Z-scores and t- scores

Journalists should have a basic understanding of z-scores and t-scores, which are often used in reporting the results of studies. A z-score, sometimes called a standard score, shows how much a particular figure differs from the mean:

Z score = (raw score – mean) / Standard deviation

The t-score, sometimes called student’s t-distribution, is closely related to z-scores. The t-score is used when the sample size is small, roughly 100 or fewer.

Practice Problem

A senior undergraduate conducting independent research at Elrond University wants to find out how many students on campus attend some religious service on a weekly basis. Select one of the five sampling methods and justify your answer.

Chapter 6: business

Business news is often big news, and this beat especially utilizes a great deal of math. Large corporations usually report earnings and results quarterly, though more detailed information, including financial statements, can be found in annual reports.

Profit and loss

The profit and loss statement, commonly called P&L, shows whether a company is making money by subtracting expenses from income. “Cost of goods sold” refers to the direct expense a business incurs by making or buying products. “Overhead” refers to the expenses not directly related to the product being made. The difference between the “cost of goods sold” and the selling price is considered the “gross margin.”

EBITDA stands for “earning before interest, taxes, depreciation and amortization” – this is also known as “operational cash flow.”

Gross margin = selling price – cost of goods sold

Gross profit = gross margin * number of items sold

Net profit = gross margin – overhead

Balance sheets

A balance sheet is a written financial statement of a company’s assets, liabilities and equity. The asset side of the balance sheet always equals the liabilities and equity side. Assets are resources owned by a company that have some economic value. Current assets include cash, investments and other liquid items of value. Long-term assets include buildings, office furniture, etc. Equity means the value of the company, and normally refers to the owners and shareholders investments in the company, capital accounts and other related assets. Liabilities are obligations, such as the loans, that need to be paid at some other date.

Assets = liabilities + equity

Ratio analysis

Ratios are calculations that analysts and business owners used to evaluate the company’s cash situation, Probability, operating efficiency and market value.

Current ratio = current assets / current liabilities

Quick ratio is a liquidity ratio that measures the ability of a company to meet its current liabilities with cash on hand.

Quick ratio = cash / current liabilities

Debt-to-asset ratio is similar to current ratio, except it includes all assets and all liabilities.

Debt-to-asset = total debt / equity

Return on total assets is a profitability ratio that measures return on the investment on all assets.

Return to assets = net income / total assets

Return on equity is a probability ratio that measures to return on the investment made equity.

Return on equity = net income / equity

Price-earnings ratio is a value ratio that measures the return of the investment based on stock price.

Price-earnings = market price / earnings

Practice Problem

Elrond University buys 1,500 bushels of pine straw from Gardenz Wholesale Co. at $5 a ton. Elrond uses 800 bushels to maintain its pristine flowerbeds. President Lampoon wants to get rid of the excess pine straw. He offers it to Low Point University for $15 a bushel. Low Point has always admired Elrond University’s superior taste in ascetics and gladly accepts. What was Elrond’s gross margin on the sale?

Chapter 7: stocks and bonds 

Stocks

Corporations sell stocks to raise cash, and people buy stocks as investments. When an individual buys a share of stock in a company, he or she becomes a partial owner of that company. The value of the company’s stock varies based on its demand.

Mutual funds are an alternative way to invest in stocks. Mutual fund companies sell shares of funds, and then use that money to buy stock in other companies.

Newspapers typically publish a stock table. In a stock table, “div” represents the most recent annual dividend that the company paid to shareholders, “PE” represents the price/earnings ratio, “last” represents the price of one share at the end of the previous day, and “change” represents how much the stock price went up or down that day.

Bonds

A bond is a loan from an investor to the government or another organization selling the bond. Unlike stocks, bonds earn interest at a set rate and are generally low risk investments. The face value of the bond is the amount that the bondholder will receive at maturity. The value of the bond on the open market fluctuates with supply and demand. The bonds current yield is its return on the investment, which therefore also fluctuates.

Current yield = (interest rate * face value) / price

Bond cost is the actual cost of a bond issued by a multiplicity.

Bond cost (interest) = amount * rate * years

Market indexes

Stock indexes track the price of certain groups of socks, allowing investors to get a snapshot of overall market conditions. Dow Jones & Co. is able to provide a snapshot of the entire stock market by monitoring the value of 30 key stocks.

NASDAQ is an acronym for the National Association of Securities Dealers Automated Quotations. It is a subsidiary of the National Association of Securities Dealers and is monitored by the Securities and Exchange Commission. NASDAQ is an automated quotation system that reports on trading of domestic stocks and bonds not listed on the stock market.

Practice problem

Janet Adamson, reporter for Elrond Daily News, noted that members of a local investment club paid $8,000 for a bond with a $9,500 face value and a 5 percent interest rate. What’s the bond’s current yeild?

Chapter 8: property taxes

Property taxes are the largest single source of income for local governments and certain other municipal organizations. The property tax rate is determined by taking the total amount of money that the governing body needs and dividing that among the property owners in that taxing district. How much each owner pays is based on the value of his or her property.

Property taxes are measured in units called mills. A mill is one-tenth of a cent. Property taxes are expressed in terms of mills levied for each dollar of the assessed valuation of the property.

Property is often taxed by more than one governing body – to prevent local governments from playing games with the tax rate, state officials often regulate the process.

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

Assessed value and appraisal value

Property taxes do not apply to the actual price of a home on the open market. The assessed value is a percentage of market value and depends on local policies.

Assessed value = appraisal value * rate

The appraisal updates real property values to reflect current market values of all taxable properties within a taxing district, as some neighborhoods fluctuate in value over time.

The percentage used to calculate the assessed value of a property might differ based on the type of property. Appraisal value is based on the property’s use and characteristics, current market conditions as determined by sales in the immediate area over time, and an official inspection of the property.

Calculating tax

Tax owed = tax rate * (assessed value of property / $100)

Divide the assessed value by $1,000, rather than $100, if the rate is based on an amount per $1,000 of assessed value.

Practice problem

The tax rate for the Town of Elrond for next year is $1.05 per $100 assessed value. If the house owned by Leopold Lampoon has an assessed value of $1,000,000, how much will he pay in taxes?

An overview of Kathleen Wickham’s ‘Math Tools for Journalists,’ chapters 1–4

by Dalton Cox

Chapter one: the language of numbers

Journalists committed to precision in reporting need to understand the language of numbers. A good place to begin is by checking the math of one’s sources – look for implausible numbers that may have been altered to give a false impression. Numerical literacy among journalists will signal to audiences the importance of numeracy.

Style Tips

It is best to consult the Associated Press Stylebook when questions arise concerning cardinal numbers.

Generally, spell out numbers below 10 and use figures for numbers above 10, but spell the words cents, million, billion, trillion, ect. When referring to money, use numerals ($5 million, 1.9 billion tons of gummy bears).

Generally rounding numbers is preferred, but not in all cases. Check the AP Stylebook. Spell out fractions less than one.

For ordinal numbers, spell first through ninth and use numerals for 10th and above.

Never begin a sentence with a number, unless indicating a year.

If an organization uses a number in their name, follow the corporate style in writing your story.

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Numbers are always used for addresses, dates, highways, percentages, speeds, temperatures, time and weight. AP Style indicates that ages are expressed with figures, but this can vary if a publication uses a different stylebook.

Use the word minus, not a dash or hyphen, to avoid confusion.

Right out numbers in a slang expression (thanks a million).

In a series, retain the appropriate style for each entry.

Chapter two: percentages

Often figures are expressed more clearly if conveyed as percentages. By providing an accurate representation of such a percentage, a reporter is helping an audience better grasp an issue.

Percentage increase/ decrease

Percentage increase/ decrease = (new figure – old figure)/ old figure

Convert the percentage by moving the decimal point two places to the right.

Example: Elon Secondary School reduced its donation to the City Squirrel Sanctuary from $4,000 to $600. By what percentage was the donation cut?

600 – 4,000 = -3,400

-3,400/ 4,000 = -0.85

The donation was cut by 85 percent. Poor squirrels.

Percentage of a whole

Percentage of a whole = subgroup/ whole group

Move the decimal point two points to the right.

Low Point University spends $1.5 million on its badminton team. The entire athletic department budget is $4 million. What percentage of the budget does the badminton team consume?

1.5 million/ 4 million = .375 = 37.5 percent

Or About 38 percent. That’s a lot of shuttlecocks.

Percentage points

It’s important to distinguish between percentage and percentage point. One percent is one one-hundredth of something. A percentage point may be a different amount.

(new figure – old figure) – old figure = change in percentage POINTS

(change in percentage points)/old figure = PERCENTAGE changed

Simple/annual interest

The amount of money borrowed is called principal. The amount of money paid for the use of principal is called interest.

Interest = principal * rate (as a decimal) * time (in years)

Compounding interest

Compounding means interest is added to the original principal and subsequent compoundings apply the interest to the principal plus the interest of the previous compoundings.

A = monthly payment

P = 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]

*^N refers to ‘N’ to the power of, which means that the result inside the bracket is multiplied N number of times.

Practice Problem

The salary of University President Leopold Lampoon was raised from $35,000 to $110,300. What percentage increase was the president’s raise?

Chapter three: statistics

After percentages, the most common numbers that a reporter will likely encounter are statistics. Sources can easily manipulate statistics, so an accurate understanding of the material is essential to informing readers of the truth.

The mean is the sum of all figures in that group, divided by the total number of figures. The median refers to the midway point in a grouping of numbers. The mode is the number appearing most frequent among a set of numbers.

A percentile is a number representing the percentage of scores that falls at or below a designated score. This is often calculated in the occurrence of test taking, such as in reporting on SAT results.

Percentile rank = (number of people at or below an individual score)/ (number of test takers)

This can easily be reversed to tell the number of people who scored at or below a certain point, if you want to know the percentile rank:

Number of people scored at or below that level = (percentile) * (number of test takers)

Standard Deviation

Standard deviation indicates how much a group of figures varies from the norm. A small deviation indicates that figures are grouped around the mean, while a high deviation shows inconsistent results.

To find standard deviation:

Subtract the mean from each score in the distribution.

Square the resulting number for each score in the set.

Calculate the mean for each of these numbers. The result of this is referred to as the variance.

Find the square root of the variance.

Probability

Probability boils down to a ratio.

For Example: The Cox Institute for Made-Up Statistics reports that nearly 2,500 Americans die from quicksand incidents each day. There are about 290 million people in the united States, so the odds of dying in a quicksand incident would be:

2,500 deaths / 290 million people = .0000086

To describe such a probability, divide one by this number:

1 / .0000086 = 116,000

So the odds of dying in a quicksand incident (based on this made-up data) is “one out of 116,000”

Some probability issues are cleaner. Winning the lottery for example is pure chance. Formula used for lottery probability:

Odds of a series of events = Odds of first event * odds of second event * odds of third event, etc.

O = odds

N = number of events

O^N = odds of a series when each is the same

Practice Problem:

In her class, Janet Andrews scored in the 40th percentile on the ACT test.

There are 50 students in her class.

Only the top 30 students will receive the school’s illustrious smarty-pants plaque.

Will Janet receive this distinguished award?

Chapter four: federal statistics

The government provides a constant stream of information of interest to the public. It is important that journalists understand the origin of these numbers and how these numbers are used.

Unemployment

Every month, the U.S. Department of Labor issues a report on unemployment in the United States. The unemployment rate is defined by the percentage of the labor force that is unemployed and actively seeking work.

Unemployment rate = (unemployed/ labor force) x 100

Inflation and Consumer Price Index

U.S. inflation is measured by the Consumer Price Index, which shows the amount of inflation in any given month for eight major product groups: food and beverage, housing, appeal, transportation and recreation. This calculation is determined by a series of surveys on the spending habits of a sample of about 30,000 U.S. families and individuals.

Monthly Inflation Rate = (Current CPI – Prior Month CPI)/ Prior Month CPI * 100

Annual inflation rate

A = Annual Inflation Rate

B = Current month CPI

C = CPI from same month in previous year

A = (B – C) / C * 100

Inflation calculator

A = Target year value, in dollars

B = Starting year value, in dollars

AC = Target year CPI

BC = Starting year CPI

A = (B / BC) * AC

Monthly compounding inflation rate formula

C = cost after one year

K = original cost

I = inflation rate

C = K (1 + [I / 12] ) ^12

Gross Domestic Product (GDP)

GDP is the value of goods and services produced by a nation’s economy.

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

The trade balance is the difference between the goods and services that a country exports to foreign countries, and its imports from abroad:

Trade balance = Exports – imports

Practice Problem:

In 1999, the Republic of Narnia exported $55.4 billion worth of fine wine and imported $16.8 billion worth. What was the trade balance in fine wine?