stats exam 1

If you want to display a group of frequencies, would you use a bar chart or a pie chart?

A Bar Chart

Explain the difference between frequency and relative frequency.

Frequency is the number of times something happens while relative frequency is the proportion of the number of times something happens compared to the whole data set

What is Class mark or class boundaries?

the values that separate different classes within a grouped data set

Class Width

the difference between the upper and lower boundaries of a class in a frequency distribution.

Give the approximate proportion of data that lies within 2 standard deviations of the mean.

>95%

Give the approximate proportion of data that lies within three standard deviations.

> 99%

When do we say that two events are independent

When P(A|B) = P(A)

Toss a coin twice

S={HH,HT,TH,TT}

Select a student from the class

Sample space: S={List of all students in the class}

Assign 3 clients to 3 salespersons (one to each)

S={(A→1,B→2,C→3),(A→1,B→3,C→2),(A→2,B→1,C→3),(A→2,B→3,C→1),(A→3,B→1,C→2),(A→3,B→2,C→1)}

Each of 3 people takes one of 3 buses at random

S={(A1,B1,C1),(A1,B1,C2),(A1,B1,C3),(A1,B2,C1),… } possible outcomes3^3 = 27

Roll two dice; sample space and probability of sum = 10

Sample space: S={ (4,6), (5,5), (6,4) }; Probability = 3/36 = 1/12.

Probability both dice are odd

Sample space: S={(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}; Probability = 9/36 = 1/4.

Are Independent Events Also Mutually Exclusive?

• No, independence means events do not affect each other’s probabilities.

• Mutually exclusive means the events cannot occur simultaneously.

• If events A and B are mutually exclusive, then: P(A and B)=0

• If they were also independent, this would imply: P(A)×P(B)=0

• This is only possible if one of the events has probability zero. So mutually exclusive events cannot be independent unless one of the events is impossible.

P(A|B)

P(A and B) / P(B) is the conditional probability of event A occurring given that event B has already occurred.

Chebychevs rule

1- 1/k² K= number of standard deviations

Combination Formula

P(A or B)

[P(A) + P(B)] - P(A and B)