Up Your Score (35 page)

Rule 7:
Chance
or
probability
is a type of ratio.

When a problem asks what the chance or probability is that a particular thing will happen, all it’s really asking you to do is to set up a ratio like this:

Here’s an example going back to the sexy underwear:

If there are 12 pairs of sexy underwear and 36 pairs of not-so-sexy underwear in a huge laundry bag, what is the probability that, at random, Bill will grab a pair of sexy underwear?

Number of times Bill could grab any pair of underwear = 12 pairs of sexy underwear + 36 pairs of not-so-sexy underwear = 48 total pairs of underwear.

= .25

Bill has a 25% chance of grabbing a pair of sexy underwear. Good luck, Bill!

Rule 8:
Average
—an average is a number that summarizes or represents all the numbers in a group.

There are three types of averages: mean, median, and mode.

Arithmetic mean
is the most commonly used average, and if you are asked to simply find the average, you should find the mean.

Arithmetic mean = (
a
+
b
+
c
+
d
. . .)/
n
where
a
,
b
,
c
,
d
. . . are the numbers and
n
is the number of numbers being averaged. For example, the mean of 3, 5, 6, 7 is

(3 + 5 + 6 + 7) / 4 = 5¼

Notice that
n
= 4 because there are four numbers in the group. Sometimes figuring out what
n
is can be tricky. Here’s an example of such a problem:

Larry’s average for the first three tests was 90%;
his average for the next two was 80%. What
was his overall average?

To find
n
in this problem you have to notice that there are
five
test scores to average: the first three can be thought of as 90s, the next two as 80s, and the average becomes

If you tried to do this by averaging 80% and 90% you’d be wrong. And Larry would be upset because you’d give him an 85% instead of an 86%.

Median
is the middle value of a group. It’s the number that would be right in the middle of the list if you arranged the numbers from smallest to largest. The median of

1, 4, 56, 59, 342, 697, 3455

is 59. If the number of values are even (which would mean there are two “middles”), then the median is the mean of these two middle values. The median of

3, 8, 45, 67, 107, 156, 223, 1032

is the mean of 67 and 107, or 87. (If you are given a list of numbers that is not in numerical order, put it in order before looking for the median.)

Mode
is the value or values that appears the greatest number of times. The mode of

3, 24, 95, 24, 56, 74, 61, 74, 74

is 74. The modes of

34, 46, 27, 1, 83, 46, 90, 1, 63

are 1 and 46.

1. The ratio of tattoos to nose rings in this room is 3 to 1. The number of nose rings is 12. How many tattoos are there in total, and what can we do to curb society’s fascination with bodily mutilation?

Sorry, but we can only help you on the first part of the question. Let’s set it up like a
math
problem:

a. By Rule 6 (ratio):

b. Number of nose rings = 12

c. Replace the words
nose rings
in the first step with the number 12:

Now, solve for tattoos. Tattoos = 36.

Why? Because
, right? Or 36:12 = 3:1.

2. 5 is what percent of 10?

“Wait—I haven’t done this!” you moan. Just relax—you can do it with what you already know. Change the question around to read

What percent of 10 is 5?

Of
means multiply—so something
times
10 is 5. You should be able to figure out that the something is ½. (Right? ½ × 10 is 5, isn’t it?) And ½ is 50%, so that’s the answer: 5 is 50% of 10.

Another way to set this up is using a ratio:

Solve for
x
by multiplying both sides by 100: