Math Tools- Statistics

By Laura Smith

November 3. 2008

The use of statistics is something that every journalist must be familiar with in addition to percentages. Statistics can be used in reporting for crime rates, salaries, and test scores, among other things. Because a journalist must report truthfully and accurately, it is important that any numbers used must be correct.

One component of statistics is using the mean. The mean is the average between a set of numbers. For example, if there is a list of workers’ salaries the reporter is discussing and he or she wants to tell the reader what the average salary for that job is, the mean will be used to find this. Next, there is the median. The median is number in the middle of a group of numbers, the midpoint. Finally, there is the mode. The mode is the number that appears most in a set of numbers. Mode could be used in the salary example to see the salary that is most commonly earned among workers.

 Percentiles are also used in statistics seen in reporting. A percentile is a number that stands for the percentage of scores that falls at or below the designated score. This means that if a student takes a test and scores in the 50th percentile, he or she will know that 50 percent of the other students who took the test scored the same or lower than they did. Percentile rank can be found by dividing the number of test takers from the number of people at or below an individual’s score.

 Next, reporters use the practice of standard deviation, mainly in scientific reports. It shows how much a group of figures varies from the norm. If the standard deviation is small, this means that the figures are grouped around the mean (average) consistently. An example of this is if a scientific experiment performed multiple times consistently shows the same results, the standard deviation is small.

            Percentiles are also used in statistics seen in reporting. A percentile is a number that stands for the percentage of scores that falls at or below the designated score. This means that if a student takes a test and scores in the 50th percentile, he or she will know that 50 percent of the other students who took the test scored the same or lower than they did. Percentile rank can be found by dividing the number of test takers from the number of people at or below an individual’s score.

            Next, reporters use the practice of standard deviation, mainly in scientific reports. It shows how much a group of figures varies from the norm. If the standard deviation is small, this means that the figures are grouped around the mean (average) consistently. An example of this is if a scientific experiment performed multiple times consistently shows the same results, the standard deviation is small.

Data within a standard deviation are viewed in a graph known as a bell curve. The middle of the curve and the highest point is the mean. If the bell is steeper, the standard deviation is smaller and if it is broader, the standard deviation is larger. In a typical distribution of data, 68 percent of the scores will fall within one standard deviation, 95 percent will fall within two, and 99 percent will fall within three.

Probability is also seen in reporters’ use of statistics. It can be is used in lottery numbers, traffic accidents, and fatal illnesses, among others. An example of this is if the reporter is wanting to report the probability of someone dying of lung cancer in the U.S. In this case, the reporter would divide the number of people in the U.S. by the number of daily deaths from lung cancer to get the probability. If the reporter wanted to find out the number of deaths per 100,000 people, they would divide the total population by total deaths and multiply this number by 100,000.

There is risk when reporting probabilities however. When discussing life and death matters, such as fatal illnesses or traffic accidents, there is the possibility the report can make readers nervous. Some questions that must be asked when reporting probabilities are: have the results been published in a peer-reviewed journal? What are the researcher’s affiliations and connections? Are the researchers reputable? Is the headline fair to the report?

Probability in reports discussing the lottery is a bit different however. In this case, it is purely chance. An example of this is a coin toss. Because a coin has two sides, the odds of getting heads and not tails on one toss is 1 out of 2. This is written as ½. If it was tossed two times then the odds would be ¼.  The odds of a series of events formula can be found by multiplying the odds of the first event, by the odds of the second event, by the odds of the third event.

 

 Practice Problems

 

 Chapter 1

Eight days ago, the temperature was 65 degrees. Today the temperature has varied between 70 and 71 degrees, higher than it was before. If is stayed at 71 degrees, how much lower was the temperature eight days ago? (This problem shows correct usage of the language of numbers)

 

 

Chapter 2

A Burlington police officer’s salary was raised from $42,750 to $44,000. What was the percentage increase of his raise?

           

            $44,000-$42,750 =$1,250

            $1,250 / $42,750 = 0.0292 = 2.92 %

 

 

Chapter 3

 What is the mean of the following scores of a history test?

87

75

98

95

83

94

82

 

87 + 75 + 98 + 95 + 83 + 94 + 82 = 614

614/7 = 87.7. The mean of the scores is 88 %

 

 

Chapter 4

The November 2007 CPI was 181.5. The November 2008 CPI was 179.2. What was the annual inflation rate of the month of November?

 

(181.5-179.2) / 179.2 x 100= annual inflation rate

2.3/ 179.2 x 100            

0.01283 x 100 = 1.28

Annual inflation rate = 1.3 %

 

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