Basic Math and Pre-Algebra For Dummies (89 page)

Now calculate:

So the president didn't lie. However, the skew in salaries resulted in a misleading mean.

When data values are skewed (when a few very high or very low numbers differ significantly from the rest of the data), the median can give you a more accurate picture of what's standard. Here's how to find the median of a set of data:

1. Arrange the set from lowest to highest.
   

   To find the median height of the boys in Table 
   19-3
   , arrange their five heights in order from lowest to highest.
   

   • 

2. Choose the middle number.
   

   The middle value, 59 inches, is the median average height.
   

To find the median number of words that the boys spelled correctly (refer to Table 
19-3
), arrange their scores in order from lowest to highest:

This time, the middle value is 18, so 18 is the median score.

 If you have an even number of values in the data set, put the numbers in order and find the mean of the
two middle numbers
in the list (see the preceding section for details on the mean). For instance, consider the following:

The two center numbers are 5 and 7. Add them together to get 12, and then divide by 2 to get their mean. The median in this list is 6.

Now recall the company president who makes $19,010,000 a year and his 99 employees who each earn $10,000. Here's how this data looks:

As you can see, if you wrote out all 100 salaries, the center numbers would obviously both be 10,000. The median salary is $10,000, and this result is much more reflective of what you'd probably earn if you worked at this company.

Probability
is the mathematics of deciding how likely an event is to occur. For example,

• What's the likelihood that the lottery ticket I bought will win?
  
• What's the likelihood that my new car will need repairs before the warranty runs out?
  
• What's the likelihood that more than 100 inches of snow will fall in Manchester, New Hampshire, this winter?
  

Probability has a wide variety of applications in insurance, weather prediction, biological sciences, and even physics.

 The study of probability started hundreds of years ago when a group of French noblemen began to suspect that math could help them turn a profit, or at least not lose so heavily, in the gambling halls they frequented.

You can read all about the details of probability in
Probability For Dummies,
by Deborah J. Rumsey (Wiley). In this section, I give you a little taste of this fascinating subject.

The
probability
that an event will occur is a fraction whose numerator (top number) and denominator (bottom number) are as follows (for more on fractions, flip to Chapter
9
):

In this case, the number of
target outcomes
(or
successes
) is simply the number of outcomes in which the event you're examining does happen. In contrast, the number of
total outcomes
(or
sample space
) is the number of outcomes that
can
happen.

For example, suppose you want to know the probability that a tossed coin will land heads up. Notice that there are two total outcomes (heads or tails), but only one of these outcomes is the target — the outcome in which heads comes up. To find the probability of this event, make a fraction as follows: