Math Tools Chapters 5-8

Polls and Surveys

Polls and surveys are extremely important, because they capture the sentiment of a journalist’s research on a topic or number of topics.  They are used by everyone from political candidates to marketing firms to news rooms, so being able to translate them to the audience is crucial for any journalist.  The book defines a poll as an estimate of public opinion on a single topic or issue based on representative samples of a population, while surveys are the same, but center around multiple topics or issues.

Since it is often impossible to ask every person in the population’s opinion on a matter, pollsters must use a relative sample of the population.  That is, a) the group of people asked has to be large enough to accurately portray the public opinion, and b) every person in the group must have the same chance of being questioned as anyone else in the group.  In order to get accurate readings, there are several sampling techniques that pollsters use:

  • Census, or universe sampling, is a rare form of sampling that actually does ask every person in the population.  This technique is used by the U.S. Census.
  • Cluster sampling is sampling by one are or region defined by well-defined boundaries, such as ZIP codes.  One class of Reporting for the Public Good could well represent the population of Elon journalism majors, for example.
  • Multistage sampling, often used in larger sample sizes, includes selecting a certain geographic area, then dividing that population into randomly selected subgroups.  Once the group is small enough, they are polled.
  • Systematic random sampling is a process where a random number, 15 for example, is chosen, and then every 15th person in a phone book or some other directory is chosen to be polled.
  • Quota sampling is a process in which the subjects are chosen based on certain known demographics (ex// blue collar and white collar jobs).
  • Probability sampling involved putting every person in the population in a hat and picking out names.  While time-consuming, this is still the most reliable way.

The margin of error measures the degree of accuracy, given in percent, and is determined by sample size.  The more people that are polled, the smaller the chance or incorrect statistics, or a small margin of error.

Confidence level is the level of confidence (for lack of a better term) that the researcher has in his/her data accuracy.  As the confidence level gets higher, so does the margin of error.  Confidence level and margin of error are often given to the reporter by the researcher, and it is important to include in the story, so that the reader can decide for his/herself how much value he/she puts in the pool.

A “z score,” or a standard score, shows how much a particular score deviates from the mean.  It is, obviously, used to compare figures and populations.  Z score = (raw score – mean) / standard deviation.  A “t score” or a “Student’s t distribution” is a more complex process.

Business

For small updates, most businesses release quarterly reports.  Annual reports, however, are often much more detailed and in-depth.

Financial statements, found in annual reports, are formal documents available to all those with interest in the company’s future, and gives quantitative data for how the company is spending money.  The Profit and Loss statement, or P&L is an annual report saying whether the company is making money or not, calculated by subtracting expenses from income.

“Costs of goods sold” means the amount of money spent in the actual production of the product.  If a company buys finished products for sale, that cost is often called “wholesale.”  “Overhead” is the cost of everything else – employee salaries, rent, utilities, insurance, etc.  The “gross margin” (sometimes called the markup) is how much more an item costs than the raw materials did.  When all of the subtractions from the income have been made, that number is the “net profit.”

EBITDA – Earnings before interest, taxes, depreciation, and amortization.

A balance sheet is a written financial statement of a company’s assets, liabilities, and equity, a document that shows the financial stability of the company.

Ratio analysis:

Current ratio = current assets / current liabilities

Quick ratio = cash / current liabilities

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

Debt-to-equity ratio = total debt / equity

Return on assets = net income / total assets

Return on equity = net income / equity

Price-earnings ratio = market price/share / earning/share

Stocks and Bonds

Corporations sell stocks to raise cash, and people buy stocks to make investments.  Mutual funds are related.  If a person wanted to invest in technology companies, he could either buy stock in several technology company or invest in a Mutual Fund that invests in technologies.  Terminology:

52-week high/low:  The highest and lowest the stock price has been in the past year.

Div – The most recent annual dividend the company paid, per share.

PE – Price/earnings ratio, the stock price divided by the per-share earnings reported in the last 12 months.

Change – How much the stock went up or down on that day.

A bond is a low-risk investment, often made in the government, which gains interest over time.  For example, you buy a bond with a $1,000 face value, a 5 percent interest rate, and maturity date in 30 years.  You get $50 of interest every year, and in 30 years, you receive your $1,000 back.  The current yield = (interest rate x face value) / price.

Bond cost = amount x rate x years.

The Dow Jones Industrial Average is the total value of one share each of 30 select stocks divided by the divisor, a figure which takes into account several corporate actions.

The NASDAQ is an acronym for the National Association of Securities Dealers Automated Quotations, which is an automated quotation system that reports on trading of domestic stocks and bonds.

Property Taxes

The property tax rate is determined by taking the total amount of money the governing body needs, and dividing that among the property owners in the taxing district.  People pay more or less depending on how much property they own.

Property taxes are measured in units called mills, which is is 1/10 of a cent.  They are expressed in terms of mills taxed per dollar, so one mill per dollar works out to $1 tax per $1,000.  There are many exemptions and deductions, but those depend on the district that the person lives in.  The key is to take into account reappraised houses, in order to determine the exact value of a house.  One must also realize that a property, a lot of the time, is taxed by more than one governing body.

An appraisal is determined by the property’s use, the property’s characteristics, current market conditions, and visual inspection by trained appraisers.  The assessed value is the appraisal value x rate.

Review Questions

  1. You must calculate statistics on a state-wide level about socioeconomic status.  What method of sampling would you choose and why?
  2. If Tom spent $100 on raw materials to make a cupboard, and sells the cupboard for $375, how much was Tom’s gross margin?
  3. The New York transportation system issued $10 million of 15-year bonds to pay for new buses.  If it is a 6% rate, what will the total cost for the New York transportation system?
  4. If there is a 10 mill property tax, how much will a person with a property valued at $1,000,000 have to pay?