GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

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Data Value Frequency

X f

-5 2

• 4 2

-3 1

-2 3

• 1 5

0 7

Total 20

From the frequency distribution, one can readily compute descriptive statistics:

Mean: = (-5)(2)+(-4)(2)+(-3)(1)+(-2)(3)+(-1)(5)+(0)(7) = -1. 6

20

Median: -1 ( the average of the 10th and 11th numbers)

Mode: 0 (the number that occurs most frequently)

Range: 0-(-5) = 5

Standard deviation:

9. Sets

(-5 + 1.6)

2

(2)+(-4+1.6)

2

(2)+ ... +(0+ 1.6)

2

(7) ""1.7

20

In mathematics a set is a collection of numbers or other objects. The objects are called the elements of the

set. If Sis a set having a finite number of elements, then the number of elements is denoted by I SI. Such

a set is often defined by listing its elements; for example, S = [-5, 0, 1} is a set with I S I = 3.

The order in which the elements are listed in a set does not matter; thus [-5, 0, 1} = [O, 1, - 5}.

If all the elements of a set S are also elements of a set T, then Sis a subset of T; for example,

S = [-5, 0, 1} is a subset of T= [-5, 0, 1, 4, 10}.

For any two sets A and B, the union of A and B is the set of all elements that are in A or in B or in both.

The intersection of A and B is the set of all elements that are both in A and in B. The union is denoted

by A u Band the intersection is denoted by A n B. As an example, if A = [3, 4} and B = [ 4, 5, 6}, then

A u B = [3, 4, 5, 6} and A n B = [ 4}. Two sets that have no elements in common are said to be disjoint

or mutually exclusive.