Statistics And Probability

Front 1

Mean

Back 1

Add up all the numbers, then divide by how manynumbers there are

Front 2

Median

Back 2

Place the numbers in value order and find themiddle number (or the mean of the middle two numbers)

Front 3

Mode

Back 3

Place the numbers in value order then count howmany of each number. The Mode is the number which appears most often (there canbe more than one mode

Front 4

Range

Back 4

Difference between the lowest and highest values

{4, 6, 9, 3, 7}

9-3=6

Front 5

Standard Deviation σ

Back 5

Measure of how spread out numbers are, formulais the square root of the Variance

Front 6

Variance

Back 6

Average of the squareddifferences from the mean

Work out the Mean (the simple average of thenumbers)

Then for each number: subtract the Mean andsquare the result (the squared difference).

Then work out the average of those squareddifferences.

Front 7

Scatterplots

Back 7

A Scatter (XY) Plot has points that show therelationship between two sets of data

Front 8

Pearson’s Coefficient of Correlation

Back 8

Step 1: Find the mean of x, and the mean of y

Step 2: Subtract the mean of x from every xvalue (call them "a"), do the same for y (call them "b")

Step 3: Calculate: a × b, a2and b2 for every value

Step 4: Sum up a × b, sum up a2and sum up b2

Step 5: Divide the sum of a × b by the squareroot of [(sum of a2) × (sum of b2)]

Front 9

Probability

Back 9

How likely something is to happening

Probability of something happening =

Number of ways it can happen /

Total number of outcomes

Front 10

Event

Back 10

One or more outcomes

Getting a Tail when tossing a coin

Choosing a "King" from a deck of cards(any of the 4 Kings)

Rolling an even number

Front 11

Sample Space

Back 11

All the possible outcomes of an experiment

Choosing a card from a deck = There are 52 cardsin a deck (not including Jokers). So the Sample Space is all 52 possiblecards: {Ace of Hearts, 2 of Hearts, etc... }

Front 12

Compound Event

Back 12

Combines at least two simple events

If you toss two coins, the probability ofgetting 2 heads

Front 13

Independent Event

Back 13

Not effected by previous events

You toss a coin and it comes up"Heads" three times ... what is the chance that the next tosswill also be a "Head"?

We can calculate the probability of 2 or more Independentevents by multiplying

Front 14

Dependent Event

Back 14

What happens depends on what happened before

Taking colored marbles from a bag: as you takeeach marble there are less marbles left in the bag, so the probabilities change

Front 15

Complementary Event

Back 15

All events that are NOT the event

When the event is Heads,the complement is Tails

Front 16

Conditional Event

Back 16

Dependent event that occurs only if anotherevent (on which it depends) has occurred.

Front 17

Tree Diagram

Back 17

Front 18

Permutations

Back 18

An ordered combination - Order matters

With repetition: nr

Without repetition – choices get reduced eachtime

-Use factorial 5! = 5*4*3*2*1

Front 19

Combinations

Back 19

Order doesn’t matter

With repetition

Without repetition