Statistics/Data Set/Counting Flashcards
How do we measure the degree of a set of number spread out/ disperse?
calculate the range or standard deviation
how to calculate the range?
What does the range tell you?
Last - First (from smallest -> greatest value)
how is the range different from the number of integers of a data set?
the number of integers is the range + 1 or Last - First + 1
how to calculate the standard deviation
(1) find the arithmetic mean, (2) find the differences between the mean and each of the n numbers, (3) square each of the differences, (4) find the average of the squared differences, and (5) take the nonnegative square root of this average.
The greater the standard deviation, the _____
The lower SD, the ____
the more the data spread away from the mean
the more the date clusters toward their average
If all the elements of a set A are also elements of a set B, then
A is the subset of B
For any two sets A and B, the union of A and B (A ∪ B) is
the set of all elements that are in A or in B or in both.
The intersection of A and B (A ∩ B) is
the set of all elements that are in both A and B.
Two sets that have no elements in common are said to be
disjoint or mutually exclusive
If two sets A and B are NOT disjoint/ mutually exclusive, then |A ∪ B | is
|A|+ |B| - |A ∩ B|
If A and B are disjoint/ mutually exclusive then
|A ∪ B | = | A | + | B |
For experiments in which all the individual outcomes are EQUALLY LIKELY, the probability of an event E is
the number of outcomes in E divide by total number of possible outcomes
If the event “A and B” is impossible (that is, A ∩ B has no outcomes), then
A and B are said to be mutually exclusive
If A and B are mutually exclusive events, then P (A and B) and P (A or B)
P (A and B ) = 0
P (A or B) = P(A) + P(B)
Two events A and B are said to be independent if
the outcome of one event does not influence or affect the outcome of the other event
If any independent events A and B occur, then P (A and B) and P (A or B)
P(A and B) = P(A) x P(B)
P(A or B) = P (A) + P (B)
T or F. If P (A) + P (B) is greater than 1 then A and B are not mutually exclusive
True. Because probability can’t be greater than 1 so there exists P (A and B)
If a set contains consecutive integers (odd/even or evenly spaced), then the mean is ?
mean = median = (first number + last number) /2
What is the sum of n consecutive integers?
(mean of n) x n
The Σ of n consecutive integers is always divisible by n, when?
n is odd
T or F. When n consecutive integers is an even number, the average is never an integer
T
Since the sum is divisible by n, its mean is an integer
T or F. If a mean of n consecutive integers is an integer, n is an odd number
T.
T or F. If a mean of n consecutive integers is an integer, n is an odd number
T.
What does consecutive multiples set mean?
each element in the set is the result of increment of multiples
Ex: {12,16,20,24} is a set of consecutive multiple of 4
How do you express an equation in evenly spaced integers (6, 11, 16, 21)?
a(n) = a(1) + d (n-1)
The total probability of n independent events is
the product of all probabilities of those independent events
if two events are mutually exclusive, then probability of two events is
the sum of those two probabilities of events
What happen to the SD if we decrease/ increase in all elements of a set by a constant percentage/factor?
the SD will also increase/ decrease by the same percentage/factor