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AS Mathematics > Statistics 1 > Flashcards

Statistics 1 Flashcards

0
Q

Class Midpoint

A

(UpperBound + LowerBound) / 2

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1
Q

Steps of Modelling a Mathematical Problem

A
  1. Observe a real world problem
  2. Devise a mathematical model
  3. Use the model to make predictions for the real world
  4. Experimental data is collected from the real world
  5. Compare predicted and observed outcomes
  6. Statistical tests are used to assess the model
  7. Mathematical model is improved and refined
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2
Q

Class Width

A

UpperBound - LowerBound

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3
Q

Mean

A

Sum of values / number of values

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4
Q

Combining Means

A

(N1X1) + (N2X1) / (N1+N2)

N1 = number of values in first sample
N2 = number of values in second sample
X1 = mean of first sample
X2 = mean of second sample
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5
Q

Coding

Definition

A

A kind of transformation of data

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6
Q

Coding

General Form

A

y = (x-a) / b

x = original data or mean
y = new data or mean
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7
Q

Q1

A

Lower Quartile

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8
Q

Q2

A

Median

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9
Q

Q3

A

Upper Quartile

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10
Q

Interquartile Range

A

Q3 - Q1

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12
Q

Q1

List of Data

A

4 pots

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13
Q

Q1

Data in a Table

A

4 pots

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14
Q

Q1

Data in a Grouped Table

A

1/4 nth value

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15
Q

Q2

List of Data

A

4 pots

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16
Q

Q2

Data in a Table

A

4 pots
OR
n+1/2 th value

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17
Q

Q2

Data in a Grouped Table

A

n/2 th value

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18
Q

Q3

List of Data

A

4 pots

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19
Q

Q3

Data in a Table

A

4 pots

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20
Q

Q3

Data in a Grouped Table

A

3/4n th value

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21
Q

Variance

Symbol

A

σ²

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22
Q

Standard Deviation

Symbol

A

σ

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23
Q

Variance

Equation (list of data)

A

Ex² / n - (Ex /n)²

The sum of x² divided by n
Minus
(The sum of x divided by n) all squared

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24
Q

Standard Deviation

Equation

A

√variance

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25
Q

Variance

Equation (data in a table)

A

Efx² / Ef - (Efx / Ef)²

The sum of frequency times x² divided by the sum of the frequencies
Minus
(The sum of frequency times x divided by the sum of the frequencies) all squared

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26
Q

Variance

Equation (data in a grouped table)

A

Efx² / Ef - (Efx / Ef)²

x the value of x is the midpoint of each class

The sum of frequency times x² divided by the sum of the frequencies
Minus
(The sum of frequency times x divided by the sum of the frequencies) all squared

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27
Q

Coding - Mean

±a

A

±a

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28
Q

Coding - Variance

±a

A

Not effected

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29
Q

Coding - Standard Deviation

±a

A

Not effected

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30
Q

Coding - Mean

xa

A

xa

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31
Q

Coding - Variance

xa

A

xa²

32
Q

Coding - Standard Deviation

xa

A

xa

33
Q

Coding - Mean

/a

A

/a

34
Q

Coding - Variance

/a

A

/a²

35
Q

Coding - Standard Deviation

/a

A

/a

36
Q

Frequency Density

Formula

A

Frequency Density = Frequency / ClassWidth

37
Q

Negative Skew

A

Q2 - Q1 > Q3 - Q2

mode > median > mean

38
Q

Positive Skew

A

Q2 - Q1 < Q3 - Q2

mode < median < mean

39
Q

Symmetrical Skew

A

Q2 - Q1 = Q3 - Q2

mode = median = mean

40
Q

Outlier

A

An extreme value
Greater than Q3 + (1.5 x IQR)
OR
Les than Q1 - (1.5 x IQR)

41
Q

Experiment

Definition

A

A repeatable process that gives rise to a number of outcomes

42
Q

Event

Definition

A

A collection or set of one or more outcomes

43
Q

Sample Space

Definition

A

The set of all possible outcomes of an experiment

44
Q

Probability

‘

A

Not

45
Q

Probability

U

A

Union
AND
OR

46
Q

Probability

n

A

Intersection

AND

47
Q

Addition Rule

A

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

48
Q

Multiplication Rule

A

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

49
Q

Complimentary Probability

A

P(‘A) = 1 - P(A)

50
Q

Mutually Exclusive Events

Definition

A

Events have no outcomes in common

51
Q

Mutually Exclusive Events

Formulae

A

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

P(A|B) = 0

P(AnB) = 0

52
Q

Independent Events

Definition

A

Events that have no effect on each other are independent

53
Q

Independent Events

Formulae

A

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

P(A|B) = P(A)

54
Q

Bivariate Data

Definition

A

Data that comes in pairs

55
Q

Variability of Bivariate Data

Sxx

A

Sxx = Ex² - (Ex)²/n

56
Q

Variability of Bivariate Data

Syy

A

Syy = Ey² - (Ey)²/n

57
Q

Variability of Bivariate Data

Sxy

A

Sxy = Exy - (ExEy)/n

58
Q

Product Moment Correlation Coefficient

Symbol

A

r

59
Q

Product Moment Correlation Coefficient

Formula

A

r = Sxy / √(SxxSyy)

60
Q

Product Moment Correlation Coefficient

r = 1

A

perfect positive linear correlation

61
Q

Product Moment Correlation Coefficient

r = -1

A

perfect negative linear correlation

62
Q

Product Moment Correlation Coefficient

r = 0

A

no linear correlation

63
Q

Regression Line

Definition

A

The line that minimises the distance to each point on the line and passes through (x,y)

x = mean of x
y = mean of y
64
Q

Regression Line

Formula

A

y = a + bx

a = y - bx
b = Sxy / Sxx
65
Q

Interpolation

Definiton

A

Estimating the value of the dependent variable within the range of data

66
Q

Extrapolation

Definition

A

Estimating the value of he dependent variable outside of the range of data
This can be unreliable

67
Q

Probability Distribution

Definition

A

A table showing the probability associated with each outcome of an experiment

68
Q

Discrete Random Variables

Expectation

A

E(X) = E x P(X=x)

69
Q

Discrete Random Variables

Variance

A

Var(X) = E(X²) - (E(X))² = E x² P(X=x) - (E(X))²

70
Q

Discrete Random Variables

Coding - Expectation

A

E(aX+b) = aE(X) + b

71
Q

Discrete Random Variables

Coding - Variance

A

Var(aX+b) = a² Var(X)

72
Q

Discrete Uniform Distribution

A

Each outcome has the same probability

P(X=x) = 1/n

73
Q

Discrete Uniform Distribution

Expectation

A

E(X) = (n+1) / 2

74
Q

Discrete Uniform Distribution

Variance

A

Var(X) = (n+1)(n-1) / 12

75
Q

Conditions for a Discrete Uniform Distribution

A

A discrete random variable X is defined over a set of n distinct values
Each value is equally likely

76
Q

Standard Normal Distribution

A

Z~N (0,1²)

AS Mathematics (3 decks)

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