The gre quatitative section 3 pdf

Here is a chartto indicate which quadrants contain which ordered pairs, based on their signs: LENGTHS OF HORIZONTAL AND VERTICAL SEGMENTS Two points with the same y-coordinate lie on the

■ Notice that the graph is broken into four quadrants with one point plotted in each one Here is a chart

to indicate which quadrants contain which ordered pairs, based on their signs:

LENGTHS OF HORIZONTAL AND VERTICAL SEGMENTS

Two points with the same y-coordinate lie on the same horizontal line, and two points with the same

x-coordinate lie on the same vertical line Find the distance between a horizontal or vertical segment by

taking the absolute value of the difference of the two points

Example:

Find the length of the line segment AB and the line segment BC.

Points CoordinatesSign of Quadrant (2,3)

(–2,3) (–3,–2) (3,–2)

(+,+) (–,+) (–,–) (+,–)

I II III IV

( −2,3) (2,3)

( −3,−2) (3, −2)

| 2 – 7 | = 5 = AB

| 1 – 5 | = 4 = BC

D ISTANCE OF C OORDINATE P OINTS

To fine the distance between two points, use this variation of the Pythagorean theorem:

d = (x21)– x22+ (y– y1)2

Example:

Find the distance between points (2,3) and (1,–2)

Solution:

d = (1 – 2)2 – 3)+ (–22

d = (1 + –2)2 + –32+ (–)2

d = (–1) (–5)2+2

d = 1 + 25

d = 26

(1,–2) (2,3)

(2,1)

(7,5) C

B A

(7,1)

Midpoint x = x1 +

2

x2

 Midpoint y = y1 +

2

y2



Example:

Find the midpoint of the segment AB.

Solution:

Midpoint x = 1 +25= 62= 3 Midpoint y = 2 +210= 122= 6

Therefore the midpoint of A – — Bis (3,6)

Slope

The slope of a line measures its steepness It is found by writing the change in y-coordinates of any two points

on the line over the change of the corresponding x-coordinates (This is also known as the rise over the run.)

The last step is to simplify the fraction that results

Example:

Find the slope of a line containing the points (3,2) and (8,9)

(5,10)

Midpoint

(1,2)

B

A

98––23= 75

Therefore, the slope of the line is 75

NOTE: If you know the slope and at least one point on a line, you can find the coordinate

point of other points on the line Simply move the required units determined by the slope In

the example above, from (8,9), given the slope 75, move up seven units and to the right five

units Another point on the line, thus, is (13,16)

I MPORTANT I NFORMATION ABOUT S LOPE

The following are a few rules about slope that you should keep in mind:

■ A line that rises to the right has a positive slope and a line that falls to the right has a negative slope

■ A horizontal line has a slope of 0 and a vertical line does not have a slope at all—it is undefined

■ Parallel lines have equal slopes

■ Perpendicular lines have slopes that are negative reciprocals

 D a t a A n a l y s i s R e v i e w

Many questions on the GRE will test your ability to analyze data Analyzing data can be in the form of sta-tistical analysis (as in using measures of central location), finding probability, and reading charts and graphs All these topics, and a few more, are covered in the following section Don’t worry, you are almost done! This

is the last review section before practice problems Sharpen your pencil and brush off your eraser one more time before the fun begins Next stop…statistical analysis!

(3,2)

(8,9)

numeric values is defined by the value that appears most frequently (the mode), the number that represents the middle value (the median), and/or the average of all the values (the mean)

MEAN AND MEDIAN

To find the average, or the mean, of a set of numbers, add all the numbers together and divide by the

quan-tity of numbers in the set

Average = nusmumbeorfovfavlualeuses

Example:

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

9 + 4 + 7

5

+ 6 + 4

= 3

5 0

= 6 The denominator is 5 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

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

Then, choose the middle values 3 and 5

Find the average of the numbers 3 +25= 4

The answer is 4

MODE

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 num-ber of times

Measures of Dispersion

Measures of dispersion, or the spread of a number set, can be in many different forms The two forms covered

on the GRE test are range and standard deviation

RANGE

The range of a data set is the greatest measurement minus the least measurement For example, given the

fol-lowing values: 5, 9, 14, 16, and 11, the range would be 16 – 5 = 11

STANDARD DEVIATION

As you can see, the range is affected by only the two most extreme values in the data set Standard deviation

is a measure of dispersion that is affected by every measurement To find the standard deviation of n

meas-urements, follow these steps:

1 First, find the mean of the measurements.

2 Subtract the mean from each measurement.

3 Square each of the differences.

4 Sum the square values.

5 Divide the sum by n.

6 Choose the nonnegative square root of the quotient.

Example:

When you find the standard deviation of a data set, you are finding the average distance from the mean

for the n measurements It cannot be negative, and when two sets of measurements are compared, the larger

the standard deviation, the larger the dispersion

x

6 7 7 9 15 16

x  10

4

3

3

1 5 6

(x  10)2

16 9 9 1 25 36 96

STANDARD DEVIATION =  ¯¯¯96

6 = 4

In the first column, the mean is 10