Statistics, Sets, Counting, Probability, Estimation and Series

Question 1

average or (arithmetic) mean

Answer 1

the sum of the n numbers divided by n

Question 2

median

Answer 2

order the numbers from least to greatest. If n is odd, the median is the middle number in the list. But if n is even, the median is the average of the two middle numbers.

Question 3

mode

Answer 3

the number that occurs most often in a list.

Question 4

statistics - range

Answer 4

The greatest value in data minus the least value

Question 5

Standard deviation of n numbers

Answer 5

1. Find their arithmetic mean
2. Find the differences between the mean and each of the n numbers
3. Square each difference
4. Find the average of the squared differences
5. Take the nonnegative square root of this average

Question 6

statistics - frequency

Answer 6

How many times a value occurs in a data set

Question 7

set

Answer 7

a collection of numbers or other things

Question 8

elements

Answer 8

The items in the set

Question 9

|S|

Answer 9

The number of elements in a finite set S

Question 10

S is a subset of T

Answer 10

all the elements in a set S are also in a set T. This is written as S ⊆ T or by T ⊇ S.

Question 11

union of two sets A and B

Answer 11

the set of all elements that are each in A or in B or both. The union is written as A ∪ B

Question 12

intersection of two sets A and B

Answer 12

the set of all elements that are each in both A and B. The intersection is written as A ∩ B

Question 13

Labels for two sets sharing no elements

Answer 13

disjoint or mutually exclusive

Question 14

general addition rule for two sets

Answer 14

The number of elements in the union of two finite sets S and T is the number of elements in S, plus the number of elements in T, minus the number of elements in the intersection of S and T.

|S ∪ T| = |S| + |T| - |S ∩ T|

Question 15

S and T are disjoint, then |S ∪T| =

Answer 15

|S| + |T|, since |S ∩ T| = 0.

Question 16

Counting Methods - multiplication principle

Answer 16

The number of possible choices of one element apiece from sets A_1, A_2, …, A_n is |A_1| * |A_2| * … * |A_n|

Question 17

Equations for working with factorials

Answer 17

n! = (n − 1)!(n) and (n + 1)! = (n!)(n + 1)

Question 18

permutation

Answer 18

A set of n objects has n! permutations

Question 19

Combinations

Answer 19

Question 20

event (probability)

Answer 20

A set of an experiment’s possible outcomes

Question 21

P(E)

Answer 21

The probability P(E) of an event E is a number between 0 and 1, inclusive

Question 22

E is impossible

Answer 22

P(E) = 0

Question 23

E is certain

Answer 23

P(E) = 1

Question 24

P(not E)

Answer 24

1 − P(E)

Question 25

P(E or F)

Answer 25

P(E) + P(F) - P(E and F)

Question 26

Events E and F are mutually exclusive

Answer 26

1. No outcomes are in E ∩ F. 2. The event “E and F” is impossible: P(E and F) = 0 3. The special addition rule for the probability of two mutually exclusive events is P(E or F) = P(E) + P(F)

Question 27

Two events E and F are independent

Answer 27

If neither changes the other's probability, P(E and F) = P(E)P(F)

Question 28

P(E and F)

Answer 28

= P(E∩F), P(E|F)*P(F)

Question 29

E is dependent on F if

Answer 29

P(E|F) <> P(E)

Question 30

Conditional probability

Answer 30

The probability that E occurs if F occurs. P(E | F) = |E∩F| / |F|

Question 31

If each outcome is equally likely, P(E) =

Answer 31

(the number of possible outcomes in E) / (the total number of possible outcomes)

Question 32

sequence

Answer 32

An algebraic function whose domain contains only positive integers. A function a(n) that is a sequence can be written as a_n

Question 33

The domain of an infinite sequence

Answer 33

Set of all positive integers

Question 34

series

Answer 34

the sum of a sequence’s terms.

Question 35

Infinite series

Answer 35

is the sum of the sequence’s infinitely many terms, a1 + a2 + a3 +` . . .

Question 36

Partial sum

Answer 36

The sum of the first k terms of sequence a_n. Can be written as a_1 + . . . + a_k.

Question 37

Strategy for calculating average

Answer 37

Use a fixed value. Add numbers above / below fixed value. Then subtract below from above. Average that number.