The sat skill exam 6 doc

When you find the elements that two (or more)

sets have in common, you are finding the intersection

of the sets. The symbol for intersection is: ∩.

For example, the intersection of the integers and

the whole numbers is the set of the whole numbers

itself. This is because the elements (numbers) that they

have in common are {0, 1, 2, 3, . . . .}. Consider the set

of positive even integers and the set of positive odd

integers. The positive even integers are:

{2, 4, 6, 8, . . . }

The positive odd integers are:

{1, 3, 5, 7, . . . }

If we were to combine the set of positive even

numbers with the set of positive odd numbers, we

would have the union of the sets:

{1, 2, 3, 4, 5, . . . }

The symbol for union is: ∪.

Mean, Median, and Mode

To find the average or mean of a set of numbers, add

all of the numbers together and divide by the quantity

of numbers in the set.

Average = qu

n

a

u

n

m

ti

b

ty

er

o

s

f

e

s

t et

Example:

Find the average of 9, 4, 7, 6, and 4.

9+4+7

5

+6+4 =

3

5

0

= 6

(because there are 5 numbers in the set)

To find the median of a set of numbers, arrange the

numbers in ascending order and find the middle value.

■ If the set contains an odd number of elements,

then simply choose the middle value.

Example:

Find the median of the number set: 1, 5, 3, 7, 2.

First, arrange the set in ascending order: 1, 2, 3,

5, 7, and then, choose the middle value: 3. The

answer is 3.

■ If the set contains an even number of elements,

simply average the two middle values.

Example:

Find the median of the number set: 1, 5, 3, 7, 2, 8.

First, arrange the set in ascending order: 1, 2, 3, 5,

7, 8, and then, choose the middle values 3 and 5.

Find the average of the numbers 3 and 5:

3 +

2

5

= 4. The answer is 4.

The mode of a set of numbers is the number that

occurs the greatest number of times.

Example:

For the number set 1, 2, 5, 3, 4, 2, 3, 6, 3, 7, the

number 3 is the mode because it occurs the

most number of times.

Percent

A percent is a measure of a part to a whole, with the

whole being equal to 100.

■ To change a decimal to a percentage, move the

decimal point two units to the right and add a

percentage symbol.

Examples:

.45 = 45% .07 = 7% .9 = 90%

■ To change a percentage to a decimal, simply move

the decimal point two places to the left and elimi￾nate the percentage symbol.

Examples:

64% = .64 87% = .87 7% = .07

■ To change a fraction to a percentage, first change

the fraction to a decimal. To do this, divide the

numerator by the denominator. Then change the

decimal to a percentage.

Examples:

4

5

= .80 = 80%

2

5

= .4 = 40%

1

8

= .125 = 12.5%

–THE SAT MATH SECTION–

117

5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 117