# Maths - Stats Flashcards Preview

## Physics > Maths - Stats > Flashcards

Flashcards in Maths - Stats Deck (24)
1
Q

Skewness

A

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

2
Q

Skewness formula

A

3(mean - median) divided by standard deviation

0 = symmetrical

+ = positive skew

• = negative skew
3
Q

Linear interpolation

A

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

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

4
Q

Standard deviation

A

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

Not affected by transformations

5
Q

Regression line

A

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

6
Q

Extrapolation

A

Estimating a value outside the data you have

Extrapolated values are unreliable

7
Q

Outliers

A

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

8
Q

Standardising scores

A

A means of comparison between data values from different data sets

Standardised scores = (X - mean)/SD

9
Q

Conditions of binomial distributions

A

Two possible outcomes

Fixed number of trials - n

Trials are independent

The probability of success for each experiment is constant

10
Q

Conditions of geometric distributions

A

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

11
Q

Geometric - P(X>x)

A

= q^x

12
Q

Geometric - P(X < or = x)

A

= 1-q^x

13
Q

Geometric - P(X > or = x)

A

= q^(x-1)

14
Q

Conditions for a normal distribution

A

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

15
Q

Standardising a normal variable

A

Z = (X-u)/SD

16
Q

Correlation

A

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

17
Q

Combinations and permutations differences

A

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

Permutations are ordered arrangements of a set of items

18
Q

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

A

E(X) = sum of xp

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

19
Q

DRV: Variance

A

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

Standard deviation is just the square root of the variance

20
Q

Mutually exclusive

Independent

A

When two events cannot happen at the same time

When one event has no effect on the other

21
Q

Regression line x on y formula

A

x = a + by

where a = mean x - mean y b

where b = Sxy/Syy

22
Q

Geometric - P(X < x)

A

1 - q^(x-1)

23
Q

How to tell if two events are mutually exclusive?

A

They can’t happen at the same time

Hence P (A inersect B) = 0

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

24
Q

How to tell if two events are independent?

A

One event has no effect on the other

P(A/B) = P(A)

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