Basic Math and Pre-Algebra For Dummies (87 page)

Here
b
is the base and
h
is the height. In this case, you have a right triangle, so the base is the distance from
F
to
T,
and the height is the distance from
S
to
F
. So you already know the area of the triangle, and you also know the length of the base. Fill in the equation:

You can now solve this equation for
h.
Start by simplifying:

Now you know that the height of the triangle is 15 meters, so you can add this information to your picture (see Figure 
18-3
).

To solve the problem, though, you still need to find out the distance from
S
to
T
. Because this is a right triangle, you can use the Pythagorean theorem to figure out the distance:

Remember that
a
and
b
are the lengths of the short sides, and
c
is the length of the longest side, called the
hypotenuse
. (See Chapter
16
for more on the Pythagorean theorem.) You can substitute numbers into this formula and solve, as follows:

So the distance from the swing set to the tree house is 25 meters.

Chapter 19

In This Chapter

Knowing how statistics works with both qualitative and quantitative data

Finding out how to calculate a percentage and the mode of a sample

Calculating the mean and median

Finding the probability of an event

Statistics and probability are two of the most important and widely used applications of math. They're applicable to virtually every aspect of the real world — business, biology, city planning, politics, meteorology, and many more areas of study. Even physics, once thought to be devoid of uncertainty, now relies on probability.

In this chapter, I give you a basic understanding of these two mathematical ideas. First, I introduce you to statistics and the important distinction between qualitative and quantitative data. I show you how to work with both types of data to find meaningful answers. Then I give you the basics of probability. I show you how the probability that an event will occur is always a number from 0 to 1 — that is, usually a fraction, decimal, or percent. After that, I demonstrate how to build this number by counting both favorable outcomes and possible outcomes. Finally, I put these ideas to work by showing you how to calculate the probability of tossing coins.

Statistics
is the science of gathering and drawing conclusions from data, which is information that's measured objectively in an unbiased, reproducible way.

An individual
statistic
is a conclusion drawn from this data. Here are some examples:

• The average working person drinks 3.7 cups of coffee every day.
  
• Only 52% of students who enter law school actually graduate.
  
• The cat is the most popular pet in the United States.
  
• In the last year, the cost of a high-definition TV dropped by an average of $575.
  

Statisticians do their work by identifying a population that they want to study: working people, law students, pet owners, buyers of electronics, whoever. Because most populations are far too large to work with, a statistician collects data from a smaller, randomly selected sample of this population. Much of statistics concerns itself with gathering data that's reliable and accurate. You can read all about this idea in
Statistics For Dummies,
2nd Edition, by Deborah J. Rumsey (Wiley).

In this section, I give you a short introduction to the more mathematical aspects of statistics.

Data
— the information used in statistics — can be either qualitative or quantitative.
Qualitative data
divides a data set (the pool of data that you've gathered) into discrete chunks based on a specific attribute. For example, in a class of students, qualitative data can include

• Each child's gender
  
• His or her favorite color
  
• Whether he or she owns at least one pet
  
• How he or she gets to and from school
  

 You can identify qualitative data by noticing that it links an attribute — that is, a quality — to each member of the data set. For example, four attributes of Emma are that she's female, her favorite color is green, she owns a dog, and she walks to school.

On the other hand,
quantitative data
provides numerical information — that is, information about quantities, or amounts. For example, quantitative data on this same classroom of students can include the following:

• Each child's height in inches
  
• Each child's weight in pounds
  
• The number of siblings each child has
  
• The number of words each child spelled correctly on the most recent spelling test
  

 You can identify quantitative data by noticing that it links a number to each member of the data set. For example, Carlos is 55 inches tall, weighs 68 pounds, has three siblings, and spelled 18 words correctly.

Qualitative data usually divides a sample into discrete chunks. As my sample — which is purely fictional — I use 25 children in Sister Elena's fifth-grade class. For example, suppose all 25 children in Sister Elena's class answer the three yes/no questions in Table 
19-1
.

Table 19-1 Sister Elena's Fifth-Grade Survey

The students also answer the question “What is your favorite color?” with the results in Table 
19-2
.

Even though the information that each child provided is non-numerical, you can handle it numerically by counting how many students made each response and working with these numbers.

Given this information, you can now make informed statements about the students in this class just by reading the charts. For instance,

• Exactly 20 children have at least one brother or sister.
  
• Nine children don't take the bus to school.
  
• Only one child's favorite color is yellow.
  

You can make more sophisticated statistical statements about qualitative data by finding out the percentage of the sample that has a specific attribute. Here's how you do so:

1. Write a statement that includes the number of members who share that attribute and the total number in the sample.
   

   Suppose you want to know what percentage of students in Sister Elena's class are only children. The chart tells you that 5 students have no siblings, and you know that 25 kids are in the class. So you can begin to answer this question as follows:
   

   • Five out of 25 children are only children.
     
2. Rewrite this statement, turning the numbers into a fraction:
   

   

   In the example,
   of the children are only children.
   

3. Turn the fraction into a percent, using the method I show you in Chapter
   12
   .
   

   You find that
   , so 20% of the children are only children.