Statistics

Question 1

Descriptive data

Answer 1

Methods for organising, summarising, and presenting data in an informative way - Graphs, tables, and numbers

Question 2

Inferential

Answer 2

Methods for drawing conclusions about a population, from a sample

Question 3

Qualitative (Categorical)

Answer 3

Nominal - Categories that cannot be ordered (eg male, female)
Ordinal - Categories that can be ordered, but the numerical difference between groups cannot always be determined (eg, low-income, middle-income, high-income)

Question 4

Quantitative (Numerical)

Answer 4

Discrete: Number
Continuous - Interval data, doesn’t contain a true zero, and ratio

Question 5

Raw data

Answer 5

Collected data that has not been organised numerically or grouped

Question 6

Frequency

Answer 6

How many times does value/category appear in the data. Can be expressed as the total number of individuals or expressed as a fraction/percentage

Question 7

Quartiles

Answer 7

Quarters
1st quartile - located where 25% of all data points are equal to or lower than this Q1 value and 75% equal to or higher

Question 8

Percentiles

Answer 8

100s

Question 9

Median quartile

Answer 9

Second quartile, 50th Percentile

Question 10

Interquartile range(IQR)

Answer 10

Q3-Q1

Question 11

Sturge’s rule

Answer 11

A rule for determining the number of classes to use in a histogram or frequency distribution table - Optimal bins
k=1+3.33*log10(n)

Question 12

Mean calculation

Answer 12

X̄=∑x,/n

Question 13

Median

Answer 13

Middle of the data set. equal halves

Question 14

Mode

Answer 14

Value which occurs with the greater frequency

Question 15

Deviation from the mean

Answer 15

Difference between each price and the average price
x,-X̄

Question 16

Symmetric distribution

Answer 16

Graph is a mirror image, Median=mean

Question 17

Left skewed

Answer 17

mode>median>mean
Negative

Question 18

Right skewed

Answer 18

mean>median>mode
Positive

Question 19

Variance

Answer 19

The average of all deviations
σ^2=∑(x,-X̄)^2,/n-1

Question 20

Standard deviation

Answer 20

A quantity expressing by how much the members of a group differ from the mean value of group
Sx=SQR(∑(x,-X̄)^2,/n-1)

Question 21

Skewness

Answer 21

=3(mean-median)/standard deviation

Question 22

Kurtosis

Answer 22

Measure of the tailedness of a distribution - how often outliners occur
=∑(x,-X̄)^4/n/S^4

Question 23

Cross-sectional data

Answer 23

Observations from a particular point in time, containing different variables

Question 24

Time series data

Answer 24

Data across time periods

Question 25

Heteroskedasticity

Answer 25

Periods of variable volatility

Question 26

Serial Correlation

Answer 26

Little to no variation in tend of time data

Question 27

Growth factor

Answer 27

Xt/Xt-1

Question 28

The approximate average growth rate

Answer 28

Average of each points growth rate over the period. (First data point cannot have an average, as such only dividing by n-1) Arithmetic equation

Question 29

The accurate growth rate

Answer 29

Geometric mean of the growth factors =^nSQRT(gt/(t-1)*gt-1/(t-2) -1

Question 30

Approximate average log equation

Answer 30

=In(Xt)-In(I1)/n-1

Question 31

Probability

Answer 31

Certainty of an outcome

Question 32

A change experiment

Answer 32

A procedure carried out under controlled conditions which has a well-defined set of possible results

Question 33

Sample space

Answer 33

All possible outcomes

Question 34

Simple set

Answer 34

A single outcome

Question 35

Compound set

Answer 35

Collection of possible outcomes

Question 36

The law of large number

Answer 36

The greater the number of turns, the closer that the outcome will approach its probability

Question 37

Independent events

Answer 37

P(A|B)=P(A) P(B|A)=P(B) P(A&B)=P(A)P(B)

Question 38

Complement rule

Answer 38

P(A)=1-P(A')

Question 39

Multiplication rules (Joint Probability) And

Answer 39

Dependent: P(A&B)=P(A)*P(B|A) Independent: P(A&B)=P(A)*P(B) Mutually exclusive: P(A&B)=0

Question 40

Addition Rules (Union of Events) Or

Answer 40

Non mutually exclusive events: P(A or B)=P(A) + P(B) - P(A&B) Mutually exclusive: P(A or B)=P(A) + P(B)

Question 41

Bayes' Theorem

Answer 41

P(A|B)=P(B|A)*P(A)/P(B)

Question 42

Factorial

Answer 42

! Multiplication of all positive consecutive numbers up to and including the original number

Question 43

Permutation

Answer 43

Number of unique ways of arranging data set where its order matters Calculated by the factorial P(n,r)=n!/(n-r)! P=6!/P(n,r)

Question 44

Combination Binomial Coefficient

Answer 44

Do not require a particular ordering of number C(n,k)=k!/r!(n-k)!

Question 45

Discrete Random variables

Answer 45

Outcome is random but can only take a limited number of outcomes

Question 46

Probability distribution function

Answer 46

Chance of picking data from random set

Question 47

Expected value

Answer 47

Long term average or mean

Question 48

Law of large numbers

Answer 48

The higher number of turns the closer the outcome will resemble the probability

Question 49

Standard deviation of a probability function

Answer 49

=SQRT(∑(x-E(X))*P(x))

Question 50

Characteristics of Binomial distribution

Answer 50

Fixed number of trials Only two possible, mutually exclusive outcomes The trials are independent X~B(n,p)

Question 51

Binomial sample space

Answer 51

number of outcomes^n

Question 52

Number of combinations

Answer 52

nCxP^x(1-p)^n-x nCx=n!/x!(n-x)! The number of combinations, times by the probability of event x to the power of its occurs, timed by the probability of event 2 to the power of its probability

Question 53

Probability density function

Answer 53

Represents the distribution of a continuous function

Question 54

Cumulative distribution function

Answer 54

Area under he curve Used to evaluate the probability of X assuming values in a particular interval Probability = Area

Question 55

Properties of Continuous probability distributions

Answer 55

The outcomes of random variable X are measured, no counted The entire area under the curve is =1 P(c

Question 56

Bell curve distribution

Answer 56

Mean=Median=Mode

Question 57

X~N(,)

Answer 57

() standard deviation

Question 58

The standard normal distribution

Answer 58

Denoted by Z Transforms any distribution X variable into Z such that Z has a mean of 0 and a standard deviation of 1 X~N(a,b) mean of X and SD of C Subtract the mean from both sides, and then divide both sides by the standard deviation

Question 59

Bell curve distribution Rule

Answer 59

68% within one standard deviation 95% within two standard deviations 99.7 within three standard deviations