Math Tools for Journalists
Math Tools for Journalists:
Polls and surveys, business, stocks and bonds and property taxes
POLLS AND SURVEYS
Polls: An estimate of public opinion on a single topic or question. They are most frequently used in political circles and are based on representative samples of the population.
Surveys: Usually an estimate of public opinion with multiple questions and used in a wide variety of social science settings. They are based on representative samples of the population.
What does this mean for reporting?
It is the reporter’s job to help readers understand the validity of polls and surveys.
Things to consider
Polls and surveys are most accurate when conducted by random selection so that every person in the population being studied has an equal opportunity to be selected. That eliminates surveys where subjects select themselves for participation such as web-surveys.
Ways of selecting samples
• Universe or population sampling: Involves everyone in the population. Example: The U.S. Census because every household is queried.
• Cluster sampling: Involves sampling in one area or region. For example, a sample of students enrolled in Media Writing would be a cluster sample of journalism majors.
• Multistage sampling: Involves selecting a specific geographic area, then randomly selecting sub-groups, then individual blocks and ten a smaller block. This is frequently used in national samples.
• Systematic random sampling: Involves selecting a specific number, ay 20, and using the phone book, city directory or other reference book and polling every 10th person.
• Quota sampling: Selects a sample based on known demographic characteristics. Example: in a poll on women with school-age children who work outside the home, a sample could be made of a proportionate number of women who work in offices and women who work in factories.
• Probability sampling: Involves putting all of the potential subjects in a hat and pulling out a certain percentage. This is an example of random selection.
Terms for reporting on polls
Margin of error: the degree of accuracy of the research based on standard norms. It is expressed as a percentage and is based on the size of a randomly selected sample. The more people polled, the smaller the possible error, thus the smaller the margin of error.
Confidence Level: The level, or percentage, at which researchers have confidence in the results of their research. The formal definition: The probability of obtaining a given result by chance. A confidence level of 90 percent means the research results had a 20 percent probability of occurring by chance. Researchers select the confidence level in advance based on pre-testing and previous research. **The confidence level should always be reported a part of the story because it gives readers a chance to assess the results for themselves.
Majority: More than 50 percent of votes cast
Straw poll: A nonscientific poll
Z scores and t scores: Often used in reporting the results of studies. A z score, also called a “standard score, shows how much a particular figure differs from the mean. In a z score, the standard deviation is used as the unit measure. The mean becomes zero and the first standard deviation is 1, the second is 2 and so on. Z scores can be negative or positive depending on the location relative to the mean. The t score, also called Student’s t distribution, is closely related to z scores and is used when the sample size is roughly 100 or fewer.
Formula: z score = (Raw score – mean) / standard deviation
Sample question:
If the raw score is 54, the mean is 23 and the standard deviation is .8, what is the z score?
Answer: (54 – 23) / .8 = 38.75
BUSINESS
Business news can include press releases, quarterly earning reports and annual reports.
Financial statements: Formal documents available to shareholders, regulatory agencies and other stakeholders interested in a company’s performance. These generally include some type of profit and loss report and a balance sheet.
Profit and loss: Commonly called P&L, one of the most important documents a company issues. It shows whether a company is making money or not, by subtracting expenses from income.
Gross margin: The difference between the “cost of goods sold” and the selling price. This can also, in retail settings, be called “mark up.”
EBITA: “Earnings before interest, taxes, depreciation and amortization.” This is a useful figure in comparing companies because it shows how much cash a company is earning without regard to items unrelated to current business.
Formulas:
Gross margin = Selling price – cost of goods sold
Gross profit = Gross margin x number of items sold
Net profit = gross margin – overhead
Sample Question:
Billy Joe worked part-time for Hello Magazine selling copies of the weekly magazine from a newsstand downtown. Joe paid $2.00 for each copy and sold each copy for $2.95. What was his gross margin?
Answer: $2.95 – $2.00 = $0.95
Ratios: Calculations that analysts and business owners use to evaluate a company’s cash situation, profitability, operating efficiency and market value.
Current ratio: a liquidity ratio that measures the ability of a company to meet its liabilities.
Formula: Current ratio = current assets / current liabilities
Quick ratio: a liquidity ratio that measures the ability of a company to meet its current liabilities with cash on hand.
Formula: Quick ratio = cash / current liabilities
Debt-to-asset ratio: similar to current ratio, except it includes all assets and all liabilities (the word debt is often used interchangeably with liabilities). It is a better indicator of the long-term health of a company than current ratio.
Formula: Debt-to-asset ratio = total debt / total assets
Return on assets: a profitability ratio that measures the return on the investment on all assets.
Formula: Return on assets = net income / total assets
Return on equity: a profitability ratio that measures the return on the investment made in equity.
Formula: Return on equity = net income / equity
Price-earnings ratio: a value ratio that measures the return of the investment based on stock price.
Formula: Price-earnings = market price/share / earnings/share
STOCKS AND BONDS
Investment Reports:
• Form 8-K – Companies are required to file an 8-K when a special event occurs, such as bankruptcy, major assets are bought or sold, etc.
• Form 10-K – The official audited annual report public companies are required to file. It shows assets, liabilities, revenue, etc.
• Form 10-Q – Quarterly reports of important financial information.
• Proxy Statement – A document sent to shareholders about matters on which the shareholders will vote.
Stock: When an individual buys a share of stock in a company, he or she becomes a part owner of the company; each share represents just a tiny portion of ownership.
Bond: A loan from an investor to the government or other organization selling the bond.
Formula: Current yield = (interest rate x face value) / price
Sample Question:
Randy Tripe paid $600 for a $900 bond with a 4% interest rate. What is his current yield?
Answer: Current yield = (4% x $900) / $600 = 6%
Bond Cost: The actual cost of a bond issued by a municipality; as a reporter this may be the more important calculation about bonds because readers will be interested in knowing how much those bonds will ultimately cost the park district.
Formula: Bond cost (interest) = amount x rate x years
Dow Jones industrial average: The total value of one share each of 30 select stocks divided by a figure called the divisor. The divisor takes into account stock dividends, splits, spin-offs and other applicable corporate actions (find the current divisor at www.cbot.com).
NASDAQ: National Association of Securities Dealers Automated Quotations, an automated quotation system that reports on trading of domestic stocks and bonds not listed in the regular stock markets.
PROPERTY TAXES
Property Taxes: The largest single source of income for local government, school districts and other municipal organizations; they pay for supplies, salaries, maintenance costs and just about every other day-to-day expense.
• Measured in units called mills ($0.001)
• Expressed in terms of mills levied for each dollar of assessed valuation of property
• Usually applied to assessed valuations, not to the actual price a home would sell for on the open market (the assessed value is a percentage of market value)
Relevance for Journalists:
Articles about property taxes often make the front page and understanding how property taxes are calculated is important for journalists.
Issues to be aware of when writing about property taxes
• Reappraisal – the purpose is to update real property values to reflect current market value of all taxable properties within a taxing district
• Taxation by more than one governing body – in some areas property owners pay only county taxes or only city taxes, in other areas property owners pay both
• Type of property – the percentage used to calculate the assessed value might differ based on the type of property
Formula: Mill levy = Taxes to be collected by the government body / assessed valuation of all property in the taxing district
Sample Question:
Suffolk’s municipal budget totals $458,400 for next year. What will the tax rate be if the assessed value of all the property in Suffolk is $82,255,000?
Answer: $458,400 / $82,255,000 = .00557 = 5.57 mills = $5.57 per $1000 assessed valuation
Assessed value: depends on local policies, which can mean credits and other adjustments; the mill levy is applied to assessed valuations.
Formula: Assessed value = appraisal value x rate
Calculating tax:
Formula: Tax owed = tax rate x (assessed value of the property / $100)
*Note: divide the assessed value by $1,000 rather than $100, if the rate is based on an amount per $1,000 of assessed value.
