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