Sat math Essentials

Unions
When you combine the elements of two (or more) sets, you are finding the 
union
of the sets. The symbol for union
is 
.
Example
The positive even integers are {2, 4, 6, 8, . . . }.
The positive odd integers are {1, 3, 5, 7, . . . }.
If we combine the elements of these two sets, we find the union of these sets:
{1, 2, 3, 4, 5, 6, 7, 8, . . . }.
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N U M B E R S A N D O P E R AT I O N S R E V I E W
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5 9

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Practice Question
Set 
P
{0,
3
7
, 0.93, 4, 6.98,
2
2
7
}
Set 
Q
{0.01, 0.15, 1.43, 4}
What is 
P
Q
?
a.
{4}
b.
{
3
7
,
2
2
7
}
c.
{0, 4}
d.
{0, 0.01, 0.15,
3
7
, 0.93, 1.43, 6.98,
2
2
7
}
e.
{0, 0.01, 0.15,
3
7
, 0.93, 1.43, 4, 6.98,
2
2
7
}
Answer
e.
P
Q
is “the union of sets 
P
and 
Q
.” The union of two sets is all the numbers from the two sets com-
bined. Set 
P
{0,
3
7
, 0.93, 4, 6.98,
2
2
7
}. Set 
Q
{0.01, 0.15, 1.43, 4}. Therefore, the union is {0, 0.01,
0.15,
3
7
, 0.93, 1.43, 4, 6.98,
2
2
7
}.
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.
mean 
Example
Find the mean of 9, 4, 7, 6, and 4.
9 + 4 + 7
5
+ 6 + 4
3
5
0
6
The denominator is 5 because there are five 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.
Then choose the middle value: 3.
The median is 3.
■
If the set contains an even number of elements, then 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.
Then choose the middle values: 3 and 5.
Find the average of the numbers 3 and 5:
3
2
5
8
2
4.
The median is 4.
sum of numbers in set
quantity of numbers in set