# Math Tools for Journalists (Chp. 1 – 6)

Sourced: Vanity Fair

The book, Math Tools for Journalists, by Kathleen Woodruff Wickham, explains the importance of having tools in statistics, understanding of the manipulation of numbers, numerical language, percentages and so much more.

Journalists have to always be prepared to make even the most tedious but important math-related news interesting to the public. Math has a bad “rep,” and good stories might be avoided by readers if the math in it is unclear, or worse yet, wrong.

Below is a summary of Chapters one through six, where I highlight the most important information from these chapters that aspiring journalists can use to better understand the math behind what they are covering.

Chapter 1: The Language of Numbers

Understanding the language of numbers, and more importantly, how to use numbers to convey information properly and efficiently, is imperative to any journalist who wants to report accurately.

Below are some tools & tips on how to best represent numbers in an article.

What is a Numeral?

• A symbol that represents a number

The 2 Types of Numerals:

• Arabic: 1, 2, 3,
• Roman: Uses letters.

1 = I, 4 = IV, 5 = V, 6 = VI, 9 = IX, 10 = X,

50 = L, 100 = C, 500 = D, 1,000 = M

i.e.

In Roman numerals the problem 11 plus 54 is spelled out as such:

XI + LIV = LXV (65)

Roman Numerals are also used for formal names. (i.e. Pope John Paul VI)

When Evaluating Numerical Documents…

• Always fact check official Reports and budgets.
• The person who has prepared the documentation might not always have the best math skills.
• Keep a keen eye on outliers, or on numbers or values that might have been manipulated to benefit the author(s) of the document.
• Evaluate the words written alongside the numbers. (i.e. few, many, several)

AP Style Number Tips…

• Spell out numbers one through 9
• Use numerals for multiple digit numbers (i.e. 10, 38)
• Use a numeral in front of a spelled out word for values like or greater than 1 million
• Round off larger numbers, when a specific number is not required
• Round off numbers to one decimal point (i.e. \$ 4.5 million)
• Spell out fractions less than one (i.e. one-quarter)
• Ages less than 10 are spelled out

Language Tips…

Know the correct definitions of these similar words:

1. Among v. Between
• Use among when subjects in question are a group or a collective
• Use between when there are two or many individual, specific items
1. Compared to Compared with
• Compared to: comparing one item with another figuratively
• With: used to examine the differences or similarities of two statistical/numerical values
1. Different from > Different than
2. Differ from Differ with
• From: when two items are different
• With: when two items or subjects are in conflict with one another
1. Don’t use the word (i.e. five-fold increase)
2. Less than v. Under
• Less than: smaller quantity
• Under: refers to a physical relationship/description
1. More than v. Over
• More than: numerical values and figures
• Over: describes spatial relationships
1. Writing “times less” does not show a numerical decrease. Do Not use this phrase.

Always keep in mind that it is better to translate numerical values into words.

Chapter 2: Percentages

Often, the best way to express or explain complicated figures clearly is through percentages.

The 5 Common Uses of Percentages and their Formulas:

1. Percentage Increase

Perc. Inc. = (new figure – old figure) / old figure

C = (A – B)/B

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

Salary Increases

Contracts for salary workers span multiple years and each year has its own specific increase. To calculate the salaries for those contracts, follow the formula below.

First Year of Contract:

Original Salary x Percent Increase = dollar amount of salary increase of the first year

Original Salary + Salary Increase = Salary for the first year of contract

Second Year:

First Year Salary x Percent Increase = dollar amount of salary increase for second year

First Year Salary + Salary Increase = Salary for the second year

Percentage Decrease

The formula is the same as that for the percentage increase, however it will result in a negative figure.

-C = (A-B)/B

For example,

The salary of the receptionists working in Orange Tech.’s headquarters declined from \$3,264 to \$244, once the company had to stop using outsourced cheap labor due to public outrage.

Values:

A= New Figure: \$244

B= Old Figure: \$3,264

Formula: (\$244 – \$3,264) / \$3,264 = -92.5%

Process:

1. \$244 – \$3,264 = \$3,020
2. \$3,020/\$3,264 = -0.925

Percentage of the Whole

Putting figures and values into context is made easier when calculating the percentage of the whole and comparing it to a specific figure.

Formula: C = A/B

Percentage of a whole = Subgroup / Whole group

Move the decimal two places to the right.

Percentage Points

Sourced: Dilbert Comics

Percent and Percentage points are not the same thing.

A Percent represents one hundredth of something. (i.e. a penny is one percent of a dollar)

A Percentage Point can be:

1. One Percent of a Hundredth (or 1 percent)

Orange Tech owns 100 percent of the market for smartphones, and its market share goes down one percentage point.

They lost 1 percent of their market share. (one of one-hundredth)

1. Something other than 1 percent

Orange Tech owns 5 percent of the market for smartphones and loses one percentage point. It’s new market share is 4 percent.

This is not equivalent to losing one percent, because the loss of 1 percentage point here means that their 4 percent market share is 20 percent lower than their previous 5 percent share. It does not represent a value of: “one of one-hundredth.”

To calculate percentage points, subtract the new percentage with the old one.

i.e.

The rate of new hires in Orange Tech was 3.3 percent in Sept. and 6.8 in October. By how many percentage points did the rate go up?

C = A – B

6.8% – 4.3% = 2.5%

Previous formulas can be used to find the percentage increase and decrease using  percentage points.

i.e.

The rate of new hires in Orange went up 4.5%, what was its percentage increase?

Our New and Old values have already been subtracted, so the first part of the formula is done.

C = (A-B)/B

C= 2.5%/3.3%= 0.581 or 58.1%

The rate of new hires rose 2.5 percentage points and 58.1% percent between September and October.

Simple/Annual Interest

Computing interest is a very common use for percentages. The interest that is charged varies, and depends on the amount of time borrowed money is kept and not paid back.

Principal is the amount of borrowed money one has acquired.

Interest is the money paid for using borrowed money.

Rate is the percent that is charged for the use of borrowed money.

The Formula for calculating interest is:

Interest = Principal x Rate (decimal) x Time (years)

I = P x R x T

i.e.

Ana García borrows \$2,000 from El Banco Popular to pay for Diesel for her electrical plant. She agrees to a 4% percent interest, payable in one payment at the end of the year. What was her interest?

P = \$2,000

R= 4% or 0.04

T= 1 year

\$80 = \$2,000 x 0.04 x 1 yr

Because Ana García is aware that the prices of Diesel keep rising, she decides to buy all the Diesel she can and pay back her loan ASAP. She does so in three months.

P = \$2,000

R= 4% or 0.04

T= .25

(Three months = .25 of a year (3/12) )

\$20 = \$2,000 x 0.04 x .25 yr

Compound Interest is when interest is added to the original principal.

Subsequent compounding occurs when the interest to the principal is added to the interest of previous compoundings.

Monthly payments are most common for consumers.

Chapter 3: Statistics

Sourced: Google, Stock Photo

Understanding statistics, and the ways in which they can be manipulated to benefit certain studies, companies or people is very important. This chapter looks at different statistics and the formulas with which to find them.

Mean

Or average is the sum of all figures in a group divided by the total number of figures.

Median

The Median can be found two different way:

1. Arrange numbers in a group from lowest to highest and find the one in the middle.
2. If you have two middle numbers (numbers that have the same number of numbers preceding and following it) and they are the same, that is your median. If the two middle numbers are not the same, add them and divide by two.

Mode

Is the number or numbers that appear most frequently in a group. If no number appears twice in a distribution of numbers, there is no mode.

Percentile

A percentile refers to the percentage of scores that fall at or below the designated score. A percentile score is founded on it’s relationship with all other scores.

i.e. If Carolina’s score for the SAT’s is on the 35th percentile, that means 35% percent of all other test takers scored the same or lower than Carolina did.

Formula for Percent Rank

Percentile Rank = (Number of people at or below individual score)/ (number of test takers)

P = A/B

Formula for number of people that Scored at or below one level

Number of people at or below an individual score= (percentile) / (number of test takers)

A = P/B

Standard Deviation

Indicates how much a group of figures varies from the norm.

A small standard deviation is equivalent to a group with figures consistently grouped around the mean. High standard deviations thus show signs of inconsistent result.

Standard deviation values are represented and written in the same way as the original data it is founded on. (i.e. dollars, decimals, etc…)

To compute standard deviation, follow the formula/steps below.

1. Subtract the mean from each score in the distribution of numbers
2. Square the resulting number for each score
3. Compute the mean for these numbers; the variance
4. Find the square root of the variance

Probability

Calculating probability is really about a ratio.

i.e.

In Purple Town, 50 people die from diabetes strikes. There are 10,000 people living in Purple Town.

50 deaths / 10,000 people = 0.005

Because, the number “0.005” is difficult to bring into context, reporters use the phrase “one out of (blank).” To find blank, divide 1 by the answer.

1/0.005= 200

Therefore, the odds of anyone in Purple Town dying on any particular day due to diabetes is one out of 200.

Instead of “one out of” some journalists use “per 100,000 people.” They follow the following formula to do so:

Deaths per 100,000 people = (Total Deaths/total population) x 100,000

When finding the probability of deaths from diseases, narrow the population by risk group to be more accurate in your reporting.

Lottery and Pure Chance

The issues of accurate probability findings diminish when calculating “pure chance” events, like winning the lottery.

When finding the possibilities tied to any series of events, the odds of a particular result is equal to the odds of each event multiplied together.

Formula, if the odds are not the same for each event in a series:

Odds of a series of events = Odds of first event x odds of second event x odds of third event x etc…

Formula, if the odds are the same for each event in a series:

(i.e. coin toss) Odds of a series = ON

when O = Odds

and N = Number of events

Chapter 4: Federal Statistics

Sourced: Google.com, Stock Photo

This chapter tries to break down and give understanding to the never-ending stream of information the federal government provides its constituents.

Unemployment

The rate of unemployment represents the percentage of the labor force that is unemployed and actively seeking work

The labor force is made up of anyone over the age of 16 who has a job, and has looked for one in the past four weeks. People who are not actively seeking work are not part of the labor force.

Employed people are those who did at least one hour of work for pay, or 15 hours of unpaid work for a family business a week before the survey was taken.

The formula for Unemployment Rate is:

Unemployment Rate = (unemployed/labor force) x 100

Inflation and Consumer Price Index

Annually, inflation might vary in its impacts on the U.S. economy. Yet, it affects the U.S. economy consistently.

Inflation in the United States is determined using the Consumer Price Index, which displays the level of inflation of eight major product groups.

The CPI can be written as an index number (a number greater than a 100) or as a monthly or annual inflation rate.

The formula to find inflation is:

Monthly inflation rate = (Current CPI – Prior Month CPI)/Prior Month CPI x 100

The formula to find the annual inflation rate is:

A = (B – C)/C x 100

When:

A= Annual inflation rate

B= Current Month CPI

C= CPI from same month in previous year

Adjusting for Inflation

This occurs when a historical figure is changed to show how it’s value would be in current dollars.

The formula for adjusting inflation is as follows:

A = (B/BC) x AC

When

A = Target year value, in dollars

B = Starting year value, in dollars

AC = Target year CPI

BC = Starting Year CPI

Gross Domestic Product

The total value of goods and services produced by a nation’s economy is the Gross Domestic Product or GDP. The higher a country’s GDP is, the healthier and more productive it is considered to be. The changes within a country’s GDP are the main focus of heads of states, journalists, scholars, and experts.

The growth rate of GDP is reported annually, while the GDP itself is reported quarterly.

The formula for GDP is:
GDP = C + I + G + NX

When

C = Consumer spending on goods and services

I = Investment spending

G = Government Spending

NX = Net Exports or the exports minus the imports

To compare the wellbeing of different country’s populations, one could use the figure real GDP per Capita.

Sourced: Google.com, Stock Photo

Trade Balance

The trade balance is the difference between the goods and services a country imports and those it exports to other countries.

The formula for Trade Balance is:

Trade Balance = Exports – Imports

i.e.

If, in December, the country Purple-Land exported \$65.3 billion dollars worth of goods and imported \$230 billion, its trade balance would be:

-164.7 = \$65.3 billion – \$230 billion

In December, Purple Land had a trade deficit of negative 164.7 billion dollars. Things aren’t going so great in Purple Land….

Chapter 5: Polls and Surveys

Evaluating and informing on the validity of polls and surveys taken is one of the most aspects of journalism.

Polls are an estimate of public opinion on a respective, individual topic or question.

Surveys are similar to polls in all but the fact that they are used in a wide array of social science studies and include a variety of questions.

Random Selection is very important when evaluating the validity of Polls and surveys. Random selection is the equal opportunity for everyone in the population to be selected.

Populations and Samples

Samples are used to represent the population being studied, and must be large enough (around 400 people) to keep the margin of error within acceptable limits.

Formulas for Selecting Samples

• Census, universe or population: when everyone in the population being studied is sampled.
• Cluster: when a group in one well-defined area (country, ZIP code, town) is sampled
• Multistage: starts by selecting one particular geographic area, then sub-groups within this area, next to individual blocks within the sub-group and then, a smaller block.
• Systematic Random: Using a random number, like 5, and calling or contacting every 5th person in state/city directory.
• Quota: this is based on demographic characteristics that pollsters are aware of.
• Probability: randomly putting all possible participants in a hat and making draws until reaching the designated percentage.

Margin of Error

A percentage which indicates a particular research’s degree of accuracy based on standard norms. It is found on the size of the random sample selected for the poll or survey.

To include the margin of error in an article, and assure the most accurate information regarding the research, make sure to add and subtract it to the particular percentages being compared.

i.e.

In a poll of 300 people, 57% said they thought Labradors where cuter than Golden Retrievers, while 43% thought the former was cuter. The margin of error in a poll or survey of 300 people is 5.7%. Then, do more people think Labradors are cuter than golden retrievers?

Team Labrador: (57% + 5.7%), (57% – 5.7%) = 62.7%- 51.3%

Team Golden: (43% + 5.7%), (43% – 5.7%) = 37.3% – 48.7

At least in this case, the statistical difference between those who thought Labradors were cuter: 62.7%- 51.3%, to those who thought Golden Retrievers were cuter: 37.3% – 48.7%, was fairly large.

Therefore it evidences there is a greater majority who believe Labs to be cuter.

Confidence Level

A percentage representing the level of confidence researchers have of the results of their research. Or, the possibility of attaining a given result by chance.

For instance, a result has a 10 percent probability of occurring by chance if confidence level of a study is 90 percent.

Confidence levels fall between 90, 95 and 98 percent and is calculated before the research begins. When it increases, so does the margin of error.

Subtract and add the confidence level to the percentages being compared in the same way that the margin of error was added and subtracted earlier to achieve the most accurate rendering of the information.

Census

In 2000, the U.S. Census was a knock-on-door and mail survey of every household in the country. There was a 67 percent return rate and the results are still coming out, slowly.

Adjusted v. Unadjusted Figures

Figures that are manipulated statistically to make up for missing data are called Adjusted figures.

For the 2000 Census, unadjusted figures were used to create congressional districts with reasonably equal populations. Adjusted figures could not be used by rule of the Supreme Court.
The states, however, may use adjusted figures based on the results to re-form legislative districts. On state levels, unadjusted and adjusted figures can only vary from 1 to 4 percent.

In the form of maps, local City planners have copies of official census tracts, which are supervised by the U.S. Census.

z Scores and t scores

Z scores, or standard scores, reflect the difference between a particular value and the mean. Their unit of measurement is the standard deviation and depending on their proximity to the mean are either negative or positive.

The formula for a Z score is:

Z score = (raw score – mean)/ standard deviation.

T scores, or Student’s t distribution, is utilized with sample sizes of 100 or fewer. A table of critical t values is required in order to calculate it.

Chapter 6: Business

This chapter focuses on breaking down the math and the reports of “Big Business.”

Sourced: Google.com, Stock Photo ]

Financial Statements

Financial statements are published in a company’s annual report and include quantitative statements about its business transactions, a balance sheet and a profit and loss report.

These statements on the company’s performance are made available to many stakeholders, such as shareholders and regulatory agencies.

Profit and Loss

This document is imperative since it shows if a company is making a profit. Profit is calculated by subtracting expenses from income.

Expenses within a company take many forms. The “cost of goods sold” refers to expenses directly related to the finished product, while “overhead” expenses refer to those that are entirely unrelated to what is being sold. (i.e. utilities and insurance)

The Gross Margin is the difference between the selling price and the “cost of goods sold.” The net profit, net earnings or net income is the total, annual or monthly difference of the overhead and the gross margin.

The formula for Gross Margin is:

Gross Margin = Selling Price – Cost of Goods Sold

The formula for Net Profit is:

Net Profit = Gross Margin – overhead

Balance Sheet

A balance sheet is a financial statement of a corporation’s liability, equity and assets. The liabilities and equities side of the balance sheet must always be equivalent to that of the assets.

The formula is expressed below.

Assets = Liabilities + Equity

This occurs because the assets of a company (i.e. real estate) minus its liabilities (owed money) equals its equity (the true value of the company).

i.e.

If Orange Tech. reported that it had \$500,000 in liabilities and \$650,000 in equity, then it’s asset is:

\$500,000 + \$650,000 = \$5,650,000

And the true worth, or equity, of Organge Tech is:

\$5,650,000 – \$500,000 = \$650,000

(Assets – Liabilities = Equity)

Ration Analysis

Ratio analysis is used as a tool of comparison between two companies or as a measure with which to examine the trends occurring within a company. More importantly, however, these calculations are used to examine the market value, operating efficiency, and profitability of a company.

Current Ratio

This is a measure of the ability a company has to meet its liabilities. The formula is:

Current Ratio = Current Assets/Current Liabilities

Quick Ratio

This is a liquidity ratio, basically, it measures whether a company can meet its current liabilities with cash on hand. The formula is written below.

Quick Ratio = Cash/Current Liabilities

Debt-to-asset Ratio

This measures a company’s ability to meet both its total assets and its total liabilities. It is a more efficient measurement of long-term health.

Debt-to-asset ratio = total debt/total assets

Debt-to-equity Ratio

This is calculated by comparing what a company owes to what it owns.

Debt-to-equity = total debt/equity

Return on Assets

This is a probability ratio, which evaluates the return on the investment, made in equity.

Return on equity = net income/equity

Price-earnings Ratio

This value, likewise to return on assets, examines the return of the investment—but based on stock price.

Price-earnings = (market price/share) / (earnings/share)