Key knowledge for statistics

Question 1

Is the product moment correlation coefficient affected by coding?

Answer 1

No

Question 2

How do you prove independence in probability?

Answer 2

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

or

P(AIB) = P(AnB)/P(B) = P(A)

Question 3

In probability if the variables are mutually exclusive what is the value of P(AnB)?

Answer 3

P(AnB) = 0

so
The addition formula will be
P(AuB) = P(A) + P(B)

Question 4

When you have to work out the mean of data before it was coded, what do you do?

Answer 4

Find the mean of the coded data, then make the mean equal to the coded formula and solve.
For example if you worked out the mean of the coded data to be 3, and the coding used was y = (x-100)/10
make (x-100)/10 = 3, then solve

mean of data without coding = 130

Question 5

When working grouped frequency distributions (eg. tables that include class such as 12 < x < 13), What do you need to include when working out class width?

Answer 5

The upper and lower bounds.

Eg.
LB= 11.5
UB = 13.5

Question 6

The height of a bar in a histogram is referred to as?

Answer 6

Frequency density

Question 7

If you have data such as
group:2 ≤ x ≤ 4 frequency: 7
how would you work out ∑fx?

Answer 7

You need to find the midpoint of x (in this case it would be 3) then times it by the frequency.

So ∑fx = 3 x 7 = 21

Question 8

If you have data such as
group:2 ≤ x ≤ 4 frequency: 7
how would you work out ∑fx^2?

Answer 8

You need to find the midpoint of x (in this case in would be 3) square it , then times it by the frequency.

So ∑fx^2 = (3)^2 x 7 = 63

Question 9

If you had to work out ∑fx^2 with data
x = 2 frequency = 5
what would you do?

Answer 9

You square the x value and times it by the frequency.

So ∑fx^2 = (2)^2 x 5 = 20

Question 10

In coding does adding or subtraction affect the standard deviation of the data?

Answer 10

No

Question 11

In coding does multiplication or division affect the standard deviation of the data?

Answer 11

Yes.
For example if the SD of the coded data is 3 and the coding formula used was y = x/10, then the SD of the data without coding would be 3 = x/10 => x = 30.

Question 12

In a histogram what is the area of the bar proportional to?

Answer 12

Frequency

Question 13

In probability what must everything in total equal?

Answer 13

1

Question 14

How would you work out the P(A’)?

Answer 14

1 - P(A)

Question 15

In correlation, if r = 1 what can you state about the data?

Answer 15

It has a perfect positive correlation.

Question 16

In correlation, if r = 0 what can you state about the data?

Answer 16

It has no correlation.

Question 17

In correlation, if r = -1 what can you state about the data?

Answer 17

It has a perfect negative correlation.

Question 18

In discrete random variables how would you work out the value of F(2.2), if you had the following data
x - p(X=x)
1  - 0.1
2 - 0.1
3 - 0.5
4 - 0.3

Answer 18

F(2.2) = F(2) = x ≤ 2

so 0.1 + 0.1 = 0.2

F(2.2) = 0.2