Measures of spread and probability

Question 1

Draw the Venn diagram for P(A)

Answer 1

See notes

Question 2

Draw the Venn diagram for P(B)

Answer 2

See notes

Question 3

Draw the Venn diagram for P(AnB)

Answer 3

See notes

Question 4

Draw the Venn diagram for P(AuB)

Answer 4

See notes

Question 5

Draw the Venn diagram for P(B’)

Answer 5

See notes

Question 6

Draw the Venn diagram for P(BnA’)

Answer 6

See notes

Question 7

Draw the Venn diagram for P(A’nB’)

Answer 7

See notes

Question 8

What is the formula for A given that B

Also written as P(A|B)

Answer 8

See notes

Question 9

What does independent mean

Answer 9

P(A) x P(B) = P(AnB)

Question 10

What does mutually exclusive mean

Answer 10

P(AnB) = 0
They can’t happen together
No overlap

Question 11

What does exhaustive mean

Answer 11

Events have probabilities that add up to 1
P(A) + P(B) = 1
P(AuB) = 1

Question 12

What is the equation for the standard deviation of a sample

Answer 12

See notes

Question 13

What are the steps for finding the median from a grouped frequency table

Answer 13

Must use boundaries not limits 
1. Add up the frequencies
2. Position the median - (n+1)/2 
3. Find which group this lies in 
4. Median:
((Position in group)/(no. in group x class width) + lower class boundary

Question 14

Why’s are the steps only an estimate of the median

Answer 14

We are assuming that all values are spread evenly throughout each group

Question 15

What is the equation for standard deviation

Answer 15

See notes

Question 16

What is the standard deviation

Answer 16

It is the average distance away from the mean

Question 17

Sketch a graph for symmetrical, positively skewed and negatively skewed data

Answer 17

See page 3 of data spread notes

Question 18

Sketch a box and whiskers diagram and say what all the lines mean

Answer 18

See page 3 of spread notes

Question 19

What does variance equal

Answer 19

The standard deviation squared

Question 20

What is the equation for the probability of ‘at least’ A

Answer 20

P(A) = 1 - P(A’)