'Middle Number' 1. Order values from smallest to biggest 2. If no. Of Values is Odd, Median = number in the middle of this list If No. of Values is even, there are 2 numbers in the middle. Median = Mean of these 2 values

Data Analysis Flashcards by Rick A

Distribution =

How frequently different values are observed in the data

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Frequency =

Number of times value appears in the data

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Frequency distribution =

Table or graph that shows values and their corresponding frequencies

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Relative Frequency =

Frequency of a value/Total Number of Data Entries

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Relative frequency distribution

Table or graph showing relative frequencies of each value

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Make predictions with the slope of trend line of a scatter plot

Take or estimate 2 points on the trend line
Work out the slope
Slope = The change in y axis per every value on the x axis
Multiply slope if needed to change x axis unit for example (for every hour, for every week etc.)

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Arithmetic Mean =

Sum of all the values/ No. Of Values

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Weighted Mean =

Sum of All UNIQUE Values/ no. Of unique values

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Weight of a value =

Frequency it appears

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Median =

‘Middle Number’

Order values from smallest to biggest
If no. Of Values is Odd, Median = number in the middle of this list

If No. of Values is even, there are 2 numbers in the middle. Median = Mean of these 2 values

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Mode

‘Most frequent’

Value that occurs most frequently in list

There can be more than one in a data set

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Positions of data

(Order data from least to greatest)

L = Least

M = Median

G = Greatest

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Quartiles

Q1, Q2(M), Q3 Split data in to 4 groups:

L - Q1

Q1 - Q2(M)

Q2(M) - Q3

Q2 - G

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Percentiles

99 percentiles split data up in 100 groups

Group 1. L - 1 percentile

Group 100. 99 percentile - G

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How to find Q1

Find median of 1st half of data (the data before median)

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How to find Q3

Find median of Second half of data (data after the median)

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Dispersion

Degree of spread of the data

Most common = range, interquartile range, standard deviation

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Range =

G - L

Greatest - Least

(Show maximal spread of data but can be effected by outliers)

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Interquartile Range =

Q3 - Q1

Shows spread of middle data. Is not effected by outliers

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Standard Deviation - measure of

Measure of spread that depends on every number in the data set (unlike ranges).

The more data is spread away from the mean - the greater the standard deviation

Sometimes called Population Standard Deviation (differentiate it from sample standard Deviation)

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How to calculate standard deviation =

Find the mean
Find the difference between each value and the mean and square it
Find the mean of these squared differences
Square root this number (take only the positive answer)

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How to find the SAMPLE Standard Deviation

Find the mean
Find the difference between each value and the mean and square it
Sum of these squared differences/ (no. of Values - 1)
Square root this number (take only the positive answer)

(Sometimes preferred for a sample of data taken from a larger ‘population’ (set) of data)

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1 , 2 , 3 Standard deviations above the mean =

Mean + 1d
Mean + 2d
Mean + 3d

d = standarde Deviation

1 , 2 , 3 Standard deviations below the mean =

Mean - 1d
Mean - 2d
Mean - 3d

d = standarde Deviation

How many standard deviations from the mean is X?

If X > Mean Mean + Rd = X If X < Mean Mean - Rd = X Where R = no. Of standard deviations So re written: R = (X - Mean) / d OR R = (X+ Mean)/ d

In any group of data all values are within ____ standard deviations of the mean

In any group of data all values are within 3 standard deviations of the mean

Set =

Collection of objects (aka members or elements) Repetitions do not count as additional elements Order does not matter

Finite set

All elements can be completely counted

Infinite Set

Can't counts all elements E.g.: set of all integers

Empty set

Has no elements/members Denoted by ∅

Non Empty Set =

A set with 1 or more members/elements

Subset

Set of numbers that are also all featured in a larger set. Example: A and B are Sets. All the elements in Set A are also in Set B. Therefore A is a SUBSET of B. Set A - {2,8} Set B - {0,2,4,6,8}

∅ is a subset of ______

∅ is a subset of every set

List =

A set that is in order Can have repeating elements (Unlike a set)

Intersections

A set formed from the parts that appear in both of 2 other sets. Example: intersection of X and Y (written as X ∩ Y) = all the elements that appear in both Set X and Set Y

Union

A set that is made up of all of the elements in 2 other sets (don't include elements twice) Example: The union of X and Y (written X ∪ Y) = all of the elements of Set X and Set Y If sets are mutually exclusive X U Y = |X| + |Y| If sets can intersect - inclusion-exclusion principle

If set have not elements in common they are said to be ____

If set have not elements in common they are said to be mutually exclusive (or disjointed). Written as X ∩ Y = ∅

Inclusion-exclusion principle

| A U B | = |A| + |B| - | A ∩ B | IF THE SETS CAN INTERSECT

Multiplication principle

If K = different possibilities for first choice M = different possibilities for second choice (that is independent of first choice) KM = different possibilities for the pair of choices Example - 5 meals 3 deserts = 15 combos (Note can be more than 2 choices)

Permutation

An order of elements Example : how many permutations of the letters A B and C are there?

Factorial

n! = n(n-1)(n-2)(n-3)..... 1 Example 3! = (3)(3-1)(3-2) = (3)(2)(1) = 6

Solving Permutation problems

1. Find number of elements (n) | 2. Calculate: n!

No. of Permutations ( objects are placed in rising order) of k Objects taken from Set n also written as: permutations of n objects taken k at a time

nPk = n!/(n-k)! Example: how many 5 digit positive integers can be using 1,2,3,4,5,6,7 if none can occur more than once? 1. n = 7 k = 5 2. 7!/(7-5)! = 2,520

No. of combinations (objects not placed in order) of k Objects taken from Set n also written as: permutations of n objects taken k at a time

nCk = n!/k!(n-k)! Example: How many ways to select a 3 person committee from group of 9? 1. n= 9 k = 3 2. 9!/3!(9-3)! = 84

Permutations nPk = Combinations nCk =

Permutations = The number of ways to select AND ORDER k Objects from a set of n Objects Combinations = The number of subsets of n that contain k objects

Sample Space

Set of all possible outcomes

Event

particular set of outcomes

Probability that event (E) occurs =

P(E) = no. of outcomes that satisfy E / Number of total possible outcomes

If event E is certain to occur P(E) =

P(E) = 1

If event E is certain not to occur P(E) =

P(E) = 0

IF event E is possible but not certain

Probability Event E wont happen =

1 - P(E)

Sum of probabilities of all possible outcomes =

The probability that both event E and F occur =

IF events E and F are independent: P (E and F) = P(E)P(F) IF events E and F are mutually exclusive (cannot occur at same time) : P (E and F) = 0 - impossible

The probability that event E or F or Both occur

IF events E and F are independent: P (E or F) = P(E) + P(F) - P (E and F) IF events E and F are mutually exclusive (cannot occur at same time) : P (E and F) = P(E) + P(F)