S1 Statistics

Question 1

Positive Skew

Answer 1

Q3 - Q2 > Q2 - Q1 or Mean > Median

Question 2

Negative Skew

Answer 2

Q2 - Q1 > Q3 - Q2 or Median > Mean

Question 3

Frequency

Answer 3

frequency density × class width

Question 4

Qualitative Variables

Answer 4

Non-numerical - e.g. red, blue or long, short etc.

Question 5

Quantitative Variables

Answer 5

Numerical - e.g. length, age, time, number of coins in pocket, etc

Question 6

Continuous Variables

Answer 6

Can take any value within a given range - e.g. height, time, age, etc.

Question 7

Discrete Variables

Answer 7

Can only take certain values - e.g. shoe size, cost in £ and p, number of coins.

Question 8

Mode

Answer 8

The value, or class interval, which occurs most often.

Question 9

Linear Interpolation

Answer 9

Median = a (start of group) + ((b - distance of beginning group to median / c - length of group) x length of group)

Question 10

Interquartile Range

Answer 10

Q3 - Q1

Question 11

Variance Formula

Answer 11

(sum of x squared / number of terms) - ((sum of x / n) squared)

Question 12

Standard Deviation

Answer 12

the square root of the variance

Question 13

Addition Law

Answer 13

P(AUB) = P(A) + P(B) - P(A intersect B)

Question 14

P(B|A)

Answer 14

P(A and B)/P(A)

Question 15

Mutually Exclusive Addition Rule

Answer 15

P(AUB) = P(A) + P(B)

Question 16

Mutually exclusive intersection

Answer 16

P(A intersect B) = 0

Question 17

Independent Event

Answer 17

One event does not effect the other

Question 18

Independent: P(A|B) =

Answer 18

P(A)

Question 19

Independent multiplication rule

Answer 19

P(A intersect B) = P(A) x P(B)

Question 20

Product Moment Correlation Coefficient (PMCC)

Answer 20

a quantity between -1.0 and 1.0 that estimates the strength of the linear relationship between two random variables. Close to -1, strong negative correlation. Close to 1, strong positive correlation.

Question 21

If scale changes for PMCC (correlation) ….

Answer 21

PMCC (correlation) is still the same

Question 22

Linear Regression

Answer 22

a statistical method used to fit a linear model to a given data set (basically best fit line)

Question 23

Reliable Regression

Answer 23

Values within the range of data

Question 24

Standard Deviation Definition

Answer 24

a measure that is used to quantify the amount of variation or dispersion of a set of data values

Question 25

Discrete Random Variable

Answer 25

Variables can only take certain values

Question 26

Uniform / Discrete Distribution

Answer 26

Every outcome has the same value

Question 27

F(x)

Answer 27

Cumulative distribution function in which probabilities up to 1

Question 28

E(x)

Answer 28

(expected value if you did it many times, like the mean) Sum of x multiplied by p

Question 29

Variance of E(x)

Answer 29

E(x^2) - E(X)^2 | Mean of the squares / square of the mean

Question 30

Expected value is affected by multiplication, division, subtraction, addition

Answer 30

E(4x+1) = 4E(x) + 1 E(1 - x) = 1 - E(x) E(x/2) = E(x) / 2

Question 31

Variance is not affected by addition and subtraction, but is affected by multiplication and division

Answer 31

``` For variance, you have to square the value Var(4x) = 16Var(x) Var(x+1) = Var(x) Var(3x+2) = 9Var(x) Var(x/2) = 1/4Var(x) ```

Question 32

Independent Rule: P(A intersect B) =

Answer 32

P(A) x P(B)

Question 33

Normal Distribution Formula

Answer 33

X ~ N(u , o^2)

Question 34

Standardizing Formula: Z =

Answer 34

(x - Mean) / standard deviation

Question 35

Explain why a histogram is appropriate for this data

Answer 35

Data is continuous

Question 36

Explain why this diagram would support the fitting of a | regression line of x onto y.

Answer 36

The points are close to an implied straight line | of best fit. There is a strong correlation within the data

Question 37

Which is the explanatory variable?

Answer 37

The variable that influences the other variable. etc. The explanatory variable is the age of each coin. This is because the age is set and the weight varies.

Question 38

Give a reason to support the use of normal distribution in this case

Answer 38

Mean and median are very close | - but when data is skewed, normal distribution will not be a good fit

Question 39

It was discovered that a coin in the original sample, which was 5 years oldl and weighed 20 grams, was a fake. State whether the exclusion of this coin would increase or decrease the value of the PMCC. Give a reason for your answer

Answer 39

It would decrease the value of the PMCC closer to -1 because removing the fake will result in a better linear fit

Question 40

Write down 2 of these events that are mutally exclusive. Give a reason for your answer

Answer 40

No overlap between events

Question 41

State whether the estimate of the mean or median is a better representation of the average speed of traffic on the road

Answer 41

- Mean is a better representation because it uses all the data OR - Median is better because data is skewed and median is not affected by extreme values

Question 42

Comment on shape of distribution

Answer 42

- skewness because ... | - symmetric because median is similar to mean

Question 43

what happens to median estimates when values are below the median change?

Answer 43

Median remains the same becomes values that change are below the median

Question 44

what happens to mean estimates when values become lower than used to?

Answer 44

Mean would lower as changes reduce total of x

Question 45

what happens to standard deviation estimates when values become lower than used to?

Answer 45

The standard deviation would increase because the data is more spread out

Question 46

Response Variable

Answer 46

The dependent variable. The variable being studied