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?

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