Basic Math and Pre-Algebra For Dummies (88 page)

Similarly, suppose you want to find out what percentage of children take the bus to school. This time, the chart tells you that 16 children take the bus, so you can write this statement:

• Sixteen out of 25 children take the bus to school.
  

Now rewrite the statement as follows:

Finally, turn this fraction into a percent: 16 ÷ 25 = 0.64, which equals 64%, so

• 64% of the children take the bus to school.
  

The
mode
tells you the most popular answer to a statistical question. For example, in the poll of Sister Elena's class (see Tables 
19-1
and
19-2
), the mode groups are children who

• Have at least one brother or sister (20 students)
  
• Own at least one pet (14 students)
  
• Take the bus to school (16 students)
  
• Chose blue as their favorite color (8 students)
  

 When a question divides a data set into two parts (as with all yes/no questions), the mode group represents more than half of the data set. But when a question divides a data set into more than two parts, the mode doesn't necessarily represent more than half of the data set.

For example, 14 children own at least one pet, and the other 11 children don't own one. So the mode group — children who own a pet — is more than half the class. But 8 of the 25 children chose blue as their favorite color. So even though this is the mode group, fewer than half the class chose this color.

 With a small sample, you may have more than one mode — for example, perhaps the number of students who like red is equal to the number who like blue. However, getting multiple modes isn't usually an issue with a larger sample because it becomes less likely that exactly the same number of people will have the same preference.

Quantitative data
assigns a numerical value to each member of the sample. As my sample — again, fictional — I use five members of Sister Elena's basketball team. Suppose that the information in Table 
19-3
has been gathered about each team member's height and most recent spelling test.

Table 19-3 Height and Spelling Test Scores

In this section, I show you how to use this information to find the mean and median for both sets of data. Both terms refer to ways to calculate the average value in a quantitative data set. An
average
gives you a general idea of where most individuals in a data set fall so you know what kinds of results are standard. For example, the average height of Sister Elena's fifth-grade class is probably less than the average height of the Los Angeles Lakers. As I show you in the sections that follow, an average can be misleading in some cases, so knowing when to use the mean versus the median is important.

 The mean is the most commonly used average. In fact, when most people use the word
average,
they're referring to the mean. Here's how you find the mean of a set of data:

1. Add up all the numbers in that set.
   

   For example, to find the average height of the five team members, first add up all their heights:
   

   • 55 + 60 + 59 + 58 + 63 = 295
     
2. Divide this result by the total number of members in that set.
   

   Divide 295 by 5 (that is, by the total number of boys on the team):
   

   

   So the mean height of the boys on Sister Elena's team is 59 inches.
   

This procedure is summed up (so to speak) in simple formula:

You can use this formula to find the mean number of words that the boys spelled correctly. To do this, plug the number of words that each boy spelled correctly into the top part of the formula, and then plug the number of boys in the group into the bottom part:

Now simplify to find the result:

As you can see, when you divide, you end up with a decimal in your answer. If you round to the nearest whole word, the mean number of words that the five boys spelled correctly is about 17 words. (For more information about rounding, see Chapter
2
.)

 The mean can be misleading when you have a strong skew in data — that is, when the data has many low values and a few very high ones, or vice versa.

For example, suppose that the president of a company tells you, “The average salary in my company is $200,000 a year!” But on your first day at work, you find out that the president's salary is $19,010,000 and each of his 99 employees earns $10,000. To find the mean, first plug the total salaries ($19,010,000 for the president plus $10,000 for each of 99 employees) into the top of the formula. Next, plug the number of employees (100) into the bottom: