Understanding Basic Statistics

Understanding basic statistics such as ratios, rates and percentages,can increase your comprehension of news articles that employ such measurements.

Do you really understand what you're reading when you breeze through a statistic laden news article? Often, people skim over the statistics presented in a news story because charts and numbers may be regarded as intimidating or boring. Statistics are just numbers used to describe a population or a way to get meaningful information from any large data set. News stories typically use statistics to enhance and add depth to the reader's understanding of the information presented. It's easy to take advantage of that once you have basic knowledge of common statistics and how they can be used.

Percentages/Ratios

These are the most common statistics used to describe a variable (the variable is the thing being measured, e.g., gender, true/false responses, age group, income). Percentages are used to describe the parts of a whole, the whole being one hundred. It is a proportional measurement. Let's look at the variable gender for an imaginary population. The breakdown looks like this: 60% male, 40% female. Based on that statistic, all of the following statements are accurate for this population:

There are more males than females.

There are 50% more males than females.

Here's how you calculate that figure:

60 males - 40 females = 20 (the difference between the two groups)

20 Æ'w40 = 0.5 (the difference divided by the number of females because you're comparing the number of males to the number of females)

0.5 x 100% = 50% (multiply the result by 100% to get the actual percentage)

The ratio is 6:4 (6 to 4) or six males for every 4 females. Ratio just means the relation between two numbers.

Mean/Median/Mode

The mean is nothing more than what we all call the average. It is used to summarize a group of numbers. For instance, the test scores from a certain class or incomes from a particular community. The mean, or average is calculated by adding up all the numbers (ex: test scores) and dividing that sum by the number of numbers. The mean gives you an indication of the most common number (test score or income for example) within that set of numbers. Yet that is not accurate to assume every time. In a test score example, a great many scores may be very high and a great many may be very low. The mean will not reflect the distribution of scores and in such a case would not be the appropriate statistic to present.



The median is another descriptive statistic that you will encounter in news articles. The median is simply the halfway point in the data set. The numbers in a data set such as test scores will be positioned in order from lowest to highest. Exactly half of the scores will be below the median and exactly half will be above it.

Another way to describe a set of numbers is to find the mode. That is the number that occurs with the most frequency in the data set. There can be more than one mode.

Rates

You're likely to encounter some data, such as national crime and health statistics, described as rates rather than percentages. Rates make descriptions and comparisons between groups and over time more accurate and meaningful. The rate is usually calculated to show the number of incidents per 100,000 people.

Any County population last year = 520,000 (T)

Number of burglaries in Any County last year = 430 (N)

The rate is figured by dividing the number (N) of burglaries by the total (T) population of Any County, then multiplying by 100,000.

(430 Æ'w520,000) x 100,000 = 82.7 burglaries per 100,000 people in Any County.

Let's use the following example to illustrate the vital difference between percentages and rates. We are looking at burglaries committed in Any County. The percentage of burglaries was 40% of all crimes for last year, but this year that increased to 50%. Did the number of burglaries increase? Not necessarily. The percentage could be higher because there was actually a drop in some other type of crime. Only the proportion has changed.

To know whether burglaries are increasing or decreasing in frequency you can look at changes in the rate. The rate of burglary in Any County last year was 82.7 per 100,000 and 40% of all crime. This year the rate is 74 per 100,00 and 50% of all crime. The incidence of burglary went down while the proportion increased.

Each statistic has something important to tell you and each one says something quite different from the other. This won't present a problem for you however, since you are now on your way to a greater understanding of basic statistics.

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