Math Tools for Journalists

Abridged version chapters 5-8

 

Polls and surveys represent public opinion regarding a specific topic or question.  Consumer surveys, for instance, help companies evaluate consumer reactions to their products.  Political polls can help predict the results of elections based on the political leanings of a randomly selected group of voters. 

However, poll and survey results can be skewed.  When reporting the results of a poll or survey, it is important to know:

1.      Who conducted the poll

2.      Who paid for the poll

3.      The wording and order of the questions

4.      The size of the sample group

5.      The method for selecting the sample group

6.      The margin of error

7.      The potential effect that news events might have had on poll results

All of these factors might affect the validity of the poll and its results. 

Because pollsters usually cannot interview an entire population, they have to select a random sample of people that is large and diverse enough to represent the population in question.  There are several methods for collecting samples.

·         The U.S. Census, for example, is a population sample because every American is supposed to participate.   

·         Cluster sampling involves one area or region.

·         Multistage sampling involves selecting a geographic area, then random sub-groups, then individual blocks within the sub-group, then an even smaller block.

·         Systematic random sampling involves sampling incremental numbers of people in a population.

·         Quota sampling selects people within a specific demographic. 

·         Probability sampling involves selecting random people through probability methods, like drawing from a hat

Margin of error, which is expressed with a percentage, represents the accuracy of a poll.  The more people polled, the smaller the margin of error will be. 

Confidence level is a percentage that represents how sure pollsters are that their results are accurate, or that their results can be replicated with a different sample. 

Reporting the margin of error and the confidence level allows readers to understand the accuracy and significance of the poll results. 

The 2000 U.S. Census had a return rate of 67 percent.  Census results include unadjusted figures as well as adjusted figures, which make up for missing data. 

Z scores: a “standard score” shows how much a figure differs from the average figure in its group.  This is also known as standard deviation. 

T scores: used with small samples, usually of 100 people or fewer. 

To determine a Z score:

z score = (raw score – mean) / standard deviation

 

When reporting business news, it becomes even more important to understand numbers.  Most corporations report their earnings quarterly, or four times per year.  They also have more extensive annual reports.  The Internal Revenue Service reviews annual reports to determine tax obligations. 

P&L- profit and loss statements simply show whether or not a company is making money. 

When reporting on profit and loss statements, it is important to remember that most of these statements are expressed in the thousands or millions.  Amounts which are subtracted will appear in parentheses.  It is less meaningful just to report a company’s numbers—it is more meaningful to report whether their numbers have risen or fallen over time. 

FASB- the Financial Accounting Standards Board had set rules and guidelines for financial accounting and the correct way to report financial information.  The Statements of Financial Accounting Standards are available at www.fasb.org.

EBITDA- Earnings before interest, taxes, depreciation and amortization.  Also called “operational cash flow.” 

To determine gross margin:

gross margin = selling price – cost of goods sold

To determine gross profit:

gross profit = gross margin x number of items sold

To determine net profit:

net profit = gross margin- overhead

 

A balance sheet outlines a company’s assets, liabilities and equity.  Assets should be equal to the liabilities and equity.

A ratio analysis represents a company’s financial standing, operating efficiency and market value.  It compares the company to others in the same field, and examines trends.  When reporting ratio analysis, it is important to mention the industry standard so that readers can understand how the company compares to others like it. 

Current ratio measures a company’s ability to pay its liabilities.

            To determine current ratio:

            current ratio = current assets / current liabilities

Quick ratio measures a company’s ability to pay for liabilities with easily accessible cash. 

            To determine quick ratio:

            quick ratio = cash / current liabilities

Debit-to-asset ratio measures all of a company’s assets against all of the liabilities.

            To determine debit-to-asset ratio:

            d-t-a ratio = total debt / total assets

Debt-to-equity ratio compares what is owed to a company and what the company owns.

            To determine d-t-e ratio:

            d-t-e ratio = total debt / equity

To determine return on assets:

            return on assets = net income / total assets

To determine return on equity:

            return on equity = net income / equity

To determine price-earnings ratio:

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

 

Stocks allow private individuals to be owners of a small portion of a corporation.  For consumers, buying stocks are an investment.  For corporations, selling stocks is a way to make money.  Mutual funds allow people to buy stocks in a variety of related corporations. 

Corporations and the government can make money by selling bonds, which is a low-risk investment that earns interest.  A corporation’s credit rating can indicate the strength of the bond.

            To determine current yield:

            current yield = (interest rate x face value) / price

            To determine bond cost:

            bond cost (interest) = amount x rate x years

           

Market indexes indicate market conditions by tracking the prices of certain groups of stocks.  The Dow Jones Industrial Average and NASDAQ are two of the biggest indexes, as well as the Russell 2000 and the S&P 500.

The Dow Jones Industrial Average is the total value of a share of 30 select stocks divided by the divisor, which accounts for stock dividends. 

 NASDAQ, or National Association of Securities Dealers Automate Quotations, reports on the trading of more than 5,000 domestic stocks and bonds.

Property taxes are the largest source of income for local governments.  The government assesses how much money it needs, and then divides that amount across local property owners to determine the property tax rate. 

Property taxes are measured in mills, or 1/10 of a cent.  Property taxes are intended to be based on the value of the property within the current market.  Different types of property (residential, commercial, agricultural, etc.) are taxed differently.  Often, more than one government body receives the money from property taxes.

            To determine mill levy=    

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

Appraisal value is based on:

·         The property’s use

·         The property’s characteristics (location, square footage, age, quality, amenities, etc.)

·         Current market conditions

·         A visual inspection of the property by appraisers

To determine assessed value:

assessed value = appraisal value x rate

To determine tax:

tax owed = tax rate x (assessed value of the property / $100)

 

1.      Gross Profit:

A woman sells 30 frozen bananas for 50 cents each.

50 cents x 30 = $15.00 gross profit

2.      Current yield on a bond:

A man paid $1,500 for a $2,000 bond with an interest rate of 5 percent.

(.05 x 2000) / 1500 = 6.6 percent current yield

3.      Property Tax

A home in Nashville has an assessed value of $25,000 and pays a tax rate of 7.5 mills. 

7.5  x ($25,000 / $100) = $1,875 in taxes owed