Maths - Stats

Question 1

Skewness

Answer 1

Mean = median = mode (symmetrical)

Mean > median > mode (positive skew)
Data is skewed to the left

Mean < median < mode (negative skew) data is skewed to the right

Question 2

Skewness formula

Answer 2

3(mean - median) divided by standard deviation

0 = symmetrical

+ = positive skew

• = negative skew

Question 3

Linear interpolation

Answer 3

Can be used to calculate median, UQ and LQ from a frequency table

= LB + (position in group/number in group X class width)

Question 4

Standard deviation

Answer 4

Square root of sum of x^2 divided by n - mean squared

When its for a frequency table its sqaure root of sum of x^2 multiplied by frequencies divided by sum of frequencies - mean^2

Sensitive to outliers

Measure of spread

Not affected by transformations

Question 5

Regression line

Answer 5

Residual - distance from a data point to the regression line

The regression line will minimise the sum of the square of these residuals

For y on x it’s horizontal residuals

For x on y it’s vertical residuals

Question 6

Extrapolation

Answer 6

Estimating a value outside the data you have

Extrapolated values are unreliable

Question 7

Outliers

Answer 7

Data points more than 2 SD from the mean

Data point more than 1.5 X IQR more than the UQ or less than the LQ

Question 8

Standardising scores

Answer 8

A means of comparison between data values from different data sets

Standardised scores = (X - mean)/SD

Question 9

Conditions of binomial distributions

Answer 9

Two possible outcomes

Fixed number of trials - n

Trials are independent

The probability of success for each experiment is constant

Question 10

Conditions of geometric distributions

Answer 10

2 possible outcomes - success and failure

Outcome of each trial is independent of the outcome of all the other trials

Probability of each trial is constant

The trials are repeated until a success occurs

Question 11

Geometric - P(X>x)

Answer 11

= q^x

Question 12

Geometric - P(X < or = x)

Answer 12

= 1-q^x

Question 13

Geometric - P(X > or = x)

Answer 13

= q^(x-1)

Question 14

Conditions for a normal distribution

Answer 14

99.9% of the data within 3 SD from the mean

95% within 2 SD from the mean

A continuous distribution which forms a symmetrical bell curve

Question 15

Standardising a normal variable

Answer 15

Z = (X-u)/SD

Question 16

Correlation

Answer 16

The measure of a relationship between two variables, greater correlation means the variable are more closely related

Question 17

Combinations and permutations differences

Answer 17

Combinations involve making a choice/ selection in which the order is unimportant

Permutations are ordered arrangements of a set of items

Question 18

Discrete random variables: expected mean and E(X^2)

Answer 18

E(X) = sum of xp

E(X^2) = sum of x^2 p

Question 19

DRV: Variance

Answer 19

Var (X) = E(X^2) - [E(X)]^2

Standard deviation is just the square root of the variance

Question 20

Mutually exclusive

Independent

Answer 20

When two events cannot happen at the same time

When one event has no effect on the other

Question 21

Regression line x on y formula

Answer 21

x = a + by

where a = mean x - mean y b

where b = Sxy/Syy

Question 22

Geometric - P(X < x)

Answer 22

1 - q^(x-1)

Question 23

How to tell if two events are mutually exclusive?

Answer 23

They can’t happen at the same time

Hence P (A inersect B) = 0

P(A U B) = P(A) + P(B)

Question 24

How to tell if two events are independent?

Answer 24

One event has no effect on the other

P(A/B) = P(A)

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