Statistics Need to Know

A larger standard deviation results in?

greater variance of the data values from the mean.

A smaller standard deviation means?

The data is close to the mean

A larger standard deviation means?

The data is further from the mean

Skewness is a way to describe the?

Symmetry or asymmetry of the distribution of values in a dataset.

Generally, if the mean is to the right of the median, the data set is?

Right-skewed or positively skewed

Generally, if the mean is to the left of the median, the data set is?

Left-skewed or negatively skewed

If the Distribution has a single peak it would be?

Unimodal

If the Distribution has a two peak it would be?

Bimodial

Bimodal distributions may be an indication that the set of data being considered is actually the

combination of two sets of data with significant differences

A uniform distribution is a ?

Distribution in which there is no distinct peak or variation in the data.

• No values or ranges are particularly more common than any other values or ranges.

What is any situation that produces a result?

An event

An event that involves two or more independent events (roling a pair of dice and taking the sum)?

Compund Event

An outcome that meets a particular set of criteria (a roll of 1 or 2 if we are looking for a number less than 3)?

Desired outcome

• or success

Two or more events whose outcomes do not affect one another (two coins tossed at the same time)?

Independent Event

Two or more events whose outcomes affect one another (two cards drawn consecutively from the same deck)?

Dependent Event

Probability of outcome is 100% or 1?

Certain outcome

Probability of outcome is 0% or 0?

Impossible outcome

Two or more outcomes whose criteria cannot all be satisfied in a single event (a coin coming up heads and tails on the same toss)?

Mutually exclusive outcome

Refers to all possible outcomes of a single event which may be discrete or continuous?

Random Variable

If the mean is higher than the median, the graph is likely?

Skewed Right

• postively

If the median is higher than the mean, the graph is likely?

Skewed Left

• negatively

Does the outlier affect the median, mode, or mean?

Only the mean

• Outlier HIGH → mean increases

• Outlier LOW → mean decreases

The total set of all possible results of a test or experiment is called a?

Sample Space

When you see the word or, what do you use?

The addition rule

• P(A or B) = P(A) + P(B) - P(A and B)

What is used to find the probability of a compound event if it is mutually exclusive (no overlap)?

P(A or B) = P(A) + P(B)

What is used to find the probability of a compound event if it is overlapping events?

P(A or B) = P(A) + P(B) - P(A and B)

What is the conditional probability (What is the probability of A happening, GIVEN THAT B already happened) equation?

P(A|B) = A and B / B

If the question says:

• “Given that…”

• “Among those who…”

• “Of the people who…”

• “If we already know…”

• “Provided that…”

The question is probably going to use what equation?

Conditional Probability

If you see the word AND and the events are independent, what rule is this and what formula do you use?

Multiplication rule

• P(A and B)=P(A)⋅P(B)

When the question says:

• “At least one…”

• “At least one of the events occurs…”

• “One or more…”

• “What is the probability something happens at least once?”

What do we use?

Complement rule

• P(at least one)=1−P(none)