# Math Tools Ch. 5-8

### Chapter 5- Polls and Surveys

Polls and surveys are heavily used and reported on by journalists. But, sometimes they can be skewed and bias and reporters need to help readers understand the polls and surveys.

Polls are an estimate of public opinion on a single topic or question and used a lot for political purposes.

Surveys are based on representative samples of the population, but usually include multiple questions. Surveys can be used a in a wide variety of settings.

Making sure a poll is reliable is important, and one way you can do it is by making sure the polls are randomly selected. Researchers have to rely on samples to get a picture of the whole population.

Margin of error and confidence level are also important to understand as a journalist. Margin of error indicates 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.

Confidence level is the level or percentage at which researchers have confidence in the results of their research.

z and t scores are also important to have a basic understanding of. A z score, or “standard score” shows how much a particular figure differs from the mean. The t score, or the student’s t distribution, is used when the sample size is small, 100 or fewer.

Formula: z score= (Raw score – mean) / standard deviation

Example: Name three things that polls need to remain unbiased.

Answer: clear wording, randomly selected participants, sampling error is reasonably small

Business beats often have the most math out of any of the others. Financial statements are formal documents that are available to shareholders, regulatory agencies and other stakeholders interested. They are found in a company’s annual report.

The profit and loss statement, P&L, is one of the most important document for a company and shows if they are making money or not. Different companies have different ways of reporting this.

Formula: Gross margin= selling price- cost of goods sold

Formula: Net profit = gross margin – overhead

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

Current ratio is a liquidity ratio that measures the ability of a company to meet its liabilities, and you will see these very often.

Formula: Current ratio = current assets / current liabilities

Math problem: Lisa paid \$1.15 for the flowers she sold in her shop and sold the flowers for \$2 per flower. What was the gross margin?

2 – 1.15= .85 cents

### Chapter 7- Stocks and Bonds

Stocks and bonds are important ways businesses raise money. Corporations sells stocks to raise cash and people buy stocks as investments. When an individual buys a share of stock in a company, they become a part owner of the company. The value of a company’s stock changes over time based on demand.

A bond is a loan from an investor to the government or other organization selling the bond and corporations and governments raise money by selling bonds. The “face value” of the bond is the amount the owner of the bond will receive at maturity. Investors often sell bonds on the open market before they mature. The “current yield” can also fluctuate.

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

Formula: Bond cost (interest) = amount x rate x years

Market averages are used to measure action on the exchanges.

Math problem: Kelly paid \$650 for a \$800 bond with a 5 percent interest rate. What is her current yield?

Current yield = (.05 X \$800) / \$650 = 6.15%

### Chapter 8- Property Taxes

Articles about property tax are often on the first page of a newspaper; they are the largest source of income for local government, school districts and other municipal organizations. Property tax is determined by taking the total amount of money the governing body needs and dividing that among the property owners in that taxing district.

Property tax is measured in units calls “mills,” which is 1/10 of a cent, or \$.001. Property taxes are usually applied to assessed valuations, not to the actual price a home would sell for.

Formula: 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 characteristics including:
• Location
• Square footage
• Number of stories
• Exterior wall type
• Year of construction
• Quality of construction
• Amenities
• Current market conditions as determined by sales in the immediate area over a specific number of years
• A visual inspection of the property by trained appraisers

Formula: assessed value = appraisal value x rate

Formula: Tax owed = tax rate x (assessed value of the property / \$100)

Math problem: Carmel’s municipal budget totals \$567,500 for next year. What will the tax rate be if the assessed value of all the property in Carmel is \$73,599,000?

\$567,500 / \$73,599,000 = .00771070 = 7.71 mills = \$7.71 per \$1,000 assessed valuation