Archive for the ‘Math Tools’ category

Math Tools For Journalists: 9-12

December 8, 2008

Directional Measurements

Because people are always curious about location, it is important to double check these details. Numbers requiring little effort to figure out can make a huge difference for readers.

To determine time, date and distance equations, the formula is distance = rate x time.

Speed and velocity are two different measurements. Speed is how fast something is moving, while velocity also indicates direction.

Something’s speed is often better represented by an average as opposed to at a particular moment in time. To determine average speed, the formula is average speed = distance / time.

Acceleration = (ending speed – starting speed) / time.

Weight and mass, like velocity and speed, are often used interchangable, but they are very different things. Mass is a measure of amount. Weight is the measure of gravity pulling on an object.

Momentum is the necessary force required to stop an object from moving. The formula is momentum = mass x velocity.

Area Measurements

Sometimes numbers aren’t a good way to explain how large something is. Instead, it is good to use comparisons so readers can visualize.

But sometimes not all readers will know what youre comparing, or exact mesasurements are better respresentations.

To determine the perimeter of something, use the formula perimeter = (2 x length) + (2x width).

The area of a square or rectangle can be determined by multiplying the length by the width.

Use square inches or feet to represent small spaces, or square feet, square yards or square rods to represent larger areas. Fields, farms and yards are represented by acres, and cities, states and counties are represented by square miles.

The radius of a circle is the distance from any edge to the middle. You need this to determine the circumference, which equals 2 π x radius. π, or pi, can be rounded to 3.14.

Volume Measurements

Liquid measurements apply to liquids in recipes, bodies of water, or other fluids.

For a rectangular solid use the formula volume = length x width x height.

Cord is a measurement that firewood is sold by. It is defined as 128 cubic feet when the wood is stacked in a line or row. It is about 8 feet long, 4 feet wide, and 4 feet high.

There are three different types of tons. A short ton is equal to 2,000 pounds. A long ton, also known as a British ton, is equal to 2,240 pounds. A metric ton is equal to 1,000 kilograms.

The Metric System

Americans don’t really have a good understanding of the metric system, but it is the measurement system used by the rest of the world. It is based on multiples of 10. Familiarity and acceptance are growing.

The meter is the basic unit for length. Mass is derived from this. The metric unit of foce is the Newton.

Each unit is 10 time larger than then next smaller unit in the metric system. Prefixes are added to make a larger or smaller factor. You can also just move the decimal point one unit left to for a bigger unit, or one unit right for a smaller unit.

There are some style moves associated with units.

Lowercase all units except Celcius. Lowercase symbols except for Liter or units derived from the name of a person or country. Capitalize symbols of prefixes that mean a million or more or lowercase those less than a million.

Only make names of units plural when the numerical value is more than one. Symbols are never pluralized.

Put a space between the number and the symbol. There is no need to hyphenate if it is used as a modifier before a noun.

In names or symbols for units having prefixes, there is no space between letters making up the symbol or name.

Do not use a period with metric unit names and symbols except at the end of the sentence.

A dot or period is used as the decimal point within numbers. Always write a zero before the decimal point in numbers less than zero.

Practice
1.    If Emily is driving on I-40 east for 5 hours, at an average speed of 72 mph, how far did she drive?
2.    If Food Lion wants to put a sidewalk around their entire parking lot, and the parking lot is 100 yards wide and 40 yards long, how big do they need to make the sidewalk to make it cover the entire perimeter?
3.    If the radius of a circle is 14 inches, how big is the circumference of it?
4.    If something is 1254 mm, how many meters is it?

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Math Tools for Journalists Ch. 5-8

November 24, 2008

Polls and Surveys

Polls and surveys can be very useful for providing readers with a view of the public opinion about something, but often these polls are skewed. So it is very important that journalists are careful to check the validity of the survey, as well as provide the readers with as much information about the survey as possible.

Information about polls journalists should always consider:

Information about who conducted the poll

Information about who paid for the poll

When and how the poll was conducted

How questions were worded, and whether or not it encouraged a particular viewpoint

The size of the sample

How the sample was selected

The margin of error

Any exterior events or conditions that may have an impact on the results

A poll can never be conducted of an entire population, so the selection of the sample is important to consider. Random selection is the most reliable type, because it means that every person in the population has an equal opportunity to be selected.

There are different types of ways to select samples:

Census, universe, or population sampling: sampling everyone in the population

Cluster sampling: sampling in one area or region

Multistage sampling: sampling sub-groups within sub-groups within a specific area or region

Systematic random sampling: selecting a number n, and polling every nth person

Quota sampling: select the sample based on demographic characteristics

Probability sampling: randomly selecting a designated percentage from all potential subjects

The margin of error and confidence level are important in translating poll results. The margin of error tells the degree of accuracy of research based on standard norms. It is a percentage based on the size of a randomly selected sample. The larger the sample, the smaller the possible error, so the smaller the margin of error. The margin of error can be determined by charts determined by statisticians.

The confidence level is complicated, but is important to reporting. Confidence level is the percentage of confidence researchers have in the results of their research. It is determined in advance, and is closely related to the margin of error.

The U.S. usually conducts a census to create congressional districts relatively equal in population. It is sent to every household in the country, but the return rate is not as high.

When this happens, figures must be manipulated to make up for the surveys that weren’t returned, resulting in adjusted figures.

Z and t scores are another element a reporter must understand. A z score shows how much a specific figure differs from the mean in order to make it easier to compare figures. The t score is used for small sample sizes.

Business

When reporting business, dealing with numbers is inevitable. But there are different situations in which statistics and numbers are more common.

Financial statements are used to update shareholders, regulatory agencies and other stakeholders about a company’s performance. It usually includes a profit and loss report and a balance sheet.

The profit and loss statement shows whether or not a company is making money. The net profit is calculated by subtracting expenses from income.

A balance sheet tells a company’s assets, liabilities and equity. For this, assets= liabilities + equity. Thus, the company’s assets (everything they own) equals liabilities (money the company owes) plus the equity (what the company is really worth).

Stocks and Bonds

Stocks and bonds are used by businesses to raise money, and it is important for journalists to report accurately on this.

When people buy stocks, it is an investment, and they become owners of tiny portions the company. A company’s stock’s value varies depending on the demand and business conditions.

Mutual fund companies sell shares, then use that money to invest in stock from other companies.

Bonds are sold by companies and governments as a loan from an investor to that company or government. They earn interest at a set rate and are low-risk investments. If owners wait until the bond matures, they receive the face value of the bond. This is often the amount the original buy pays for it.

To determine a bond’s “current yield,” or return on the investment,” use the formula: current yield = (interest rate x face value)/price.

Many bonds are tax exempt when they come from governments, so the return may be more from those. Also, the formula above doesn’t take into account reinvestment.

Reporters may be more interested in the bond cost though, and the formula for that is: bond cost (interest) = amount x rate x years.

Market averages are used to measure action on the exchanges, while stock indexes give an overall picture of market conditions.

The Dow Jones Industrial Average is one people are hearing about constantly. This is the total value of one share of each of 30 select stocks divided by a figure called the divisor. This number is used to show how the entire stock market is doing.

NASDAQ, the National Association of Securities Dealers Automated Quotations, is an automated quotation system that gives information about domestic stocks and bonds that aren’t listed on the regular stock markets.

Property Taxes

Property taxes are the largest source of income for local government, school districts and other municipal organizations. The property tax rate is generally decided depending on how much money the organization needs, and then dividing that among property owners. Owners pay a certain amount based on the value of their property (generally real estate, but sometimes includes other valuable assets).

Property taxes are usually applied to homes’ assessed valuations, not the actual prices they would sell for on the market. Reappraisal is important to update so that it reflects the current market value.

Appraisal value is based on the property’s use, certain characteristics (location, square footage, number of stories, exterior wall type, age, quality of construction and amenities), current market conditions and a visual inspection by trained appraisers.

Often property will be taxed by more than one organization – city, county, etc. Property may also be taxed with a different percentage used to calculate the assessed value.

The mill levy = taxes to be collected by the government body/assessed valuation of all property in the taxing district. This is then applied to assessed valuations. Assessed value= appraisal value x rate.

Each municipality figures its taxes differently based on local policies, so journalists should be sure to check before reporting about them.

To figure out the tax owed, divide the assessed value of the property by $100. Then multiply that by the tax rate.

Practice

1. If 200 Elon students were polled about who they voted for in the election, and 54 percent said Obama, is it appropriate to say that Obama won Elon’s vote?

2. A hot dog vendor earns $600 in one day. His cart is already paid for, but the food and wrappers cost $300, and he had to pay $25 to park his cart for the day. What was his net profit for the day?

3. Emily bought a $1,000 bond for $850 with a 4 percent interest rate. What is her current yield?

4. Elon issued $3 million worth of 5 year bonds, with 5 percent coupon, to pay for the new library. How much wil Elon pay in interest over the life of the bonds?

Ch. 1-4 Math Tools

November 3, 2008

Journalists generally don’t like numbers, but numbers and math are a necessity in reporting. It adds necessary details that if can either make the story more informative or completely destroy the credibility of an article or writer if wrong.

Language

When writing numbers in an article, the reporter has the the responsibility to work out the math for readers – readers should never have to figure it out themselves. The best way to keep it simple and easy for readers to understand is to follow basic style rules regarding when to spell out numbers and how to make them most manageable.

The following numbers should be spelled out: single digit numbers (1-9), fractions less than one, a position or order in ranking for first through ninth, the start of a sentence (unless it is a date) or if an organization spells a number out in its name.

The following numbers should be written in numerals: multiple digit numbers, position or order in ranking higher than tenth (numeral and superscript), if an organization leaves it as a numeral in its name, addresses, dates, highway destinations, percentages, speeds, temperatures, times, weights, with money, ages or slang. The word minus should also be spelled out rather than using a dash or hyphen.
A combination of numerals and words can be used for numbers larger than 1 million. A mixture of numerals and words is also appropriate in a serious of numbers.

It is good to round large numbers in writing if the specific number is unnecessary and it will make it easier for the reader. Some cases, such as deaths, require specific numbers. If a number is rounded, it should be rounded to one decimal point if possible.

Even though numbers add important information to an article, it is important to try to limit how many numbers are in each paragraph. Two or three is about the limit in body paragraphs, and one in the lede.

Percentages

Percentages are a common in journalism and can help readers have a better sense of the numbers a writer is presenting.

To determine a percentage increase or decrease, the formula is simple: Percentage increase or decrease = (new figure minus old figure) divided by old figure. Then, move the decimal to places to the right. For percent decreases, the number should be negative.

Finding the percentage of a whole can help give readers perspective of how much of an impact something has. In this case, the percentage of a whole= the subgroup divided by the whole group. Again, the decimal point should be moved two places to the right.

A percentage point is complete different from a percent. A change in percentage points would be changing from 8 percent to 9 percent, as opposed to determining that 2 is 25 percent of 8. To determine percentage points, subtraction is all that is needed.

To convert a fraction to a percentage, divide the numerator by the denominator, then move the decimal point two places to the right.

For interest, proper vocabulary is necessary. The principal is the amount of money borrowed, and the money paid in addition to this is the interest. The rate is the percent charged for interest.

To determine simple interest, the interest =  the principal times the rate (as a decimal) times the number of years.

Compounding interest, another type of interest occurs when the interest is added to the original principal, and then the interest is re-calculated the next time from the result of that.
While interest is usually annual, payments on loans are usually monthly. These are compounded, and the formula is more complex, and an advanced or online calculator makes it much easier.

Statistics

Statistics can be helpful, but must always be used with the understanding that they can be easily manipulated to support what someone wants to present.

There are different types of averages, and the most common is the mean. To find the mean, simply add all of the numbers together, then divide by the number of numbers. To find the median, arrange all of the numbers in ascending or descending order, then find the middle point. If there is an even number of number, find the mean of the two middle numbers. The mode is the number that appears most often in a group of numbers. Which should be used for what articles should be determined on a case-to-case basis so as to present the story most accurately.

Percentiles can also help readers determine where something ranks on a scale. To determine a percentile rank, divide the number of people at or below an individual score by the number of test takers. To determine how many people scored below that level, multiply instead of divide.

To determine how similar a number or group of numbers is to the rest of the numbers, standard deviation can be used.

Probability shows how likely something is to occur. To determine the probability, divide the number of people or things affected by the total number of people or things. To make this a “one out of ##” statement, divide one by the probability.

Federal Statistics

Even with an abundance of information available for reporters, it is impossible to present the figures associated with the federal government if the reporter does not know how to use the information.

Unemployment is a common concern in journalism, but to use the figures associated with it, it is important to know how and why the numbers are calculated. To determine the unemployment rate, divide the number of unemployed people by the labor force (anyone older than 16 who has a job or has looked for one in the past four weeks) then multiply by 100. When using these numbers though, it is important to keep in mind that the Department of Labor is in charge of calculating these numbers from a small sample.

Inflation, a common trend, also appears in reporting often. The Consumer Price Index can be used to present this. To adjust for this trend when comparing current prices to older ones, there is a calculator available on the Bureau of Labor Statistics Web site.

The Gross Domestic Product helps readers determine the value of a nation’s economy’s production.This can be used to determine whether the economy of a country is in good or bad health. This information is collected and computed by the U.S. Bureau of Economic Analysis.

Trade balance compares the number of imports to the number of exports. With a compilation of information from a variety of sources, the trade balance = the number of exports minus the number of imports. If it is negative, it is considered a trade deficit.

Practice
If the University of Tennessee football team has played 11 games this fall, but only won 4, what percentage of games has the team won?

In September 52.2 percent of Elon students looked at JuicyCampus.com weekly. In October, 21.2 percent of students still looked at Juicy Campus.com weekly. How many percentage points has this changed?

If three copy editors get paid $20 per issue, five designers get paid $25 per issue, and six section editors get paid $30 per issue, what is the average salary for The Pendulum executive staff? Which average should be used?

For the medical school she is applying to, Sarah should be in the in the 94th percentile of test takers to have a chance. If 1,736 students took the test, how many people have to score the same or below her?