Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

AS Mathematics > Statistics 1 > Flashcards

Statistics 1 Flashcards

0
Q

Class Midpoint

A

(UpperBound + LowerBound) / 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Class Width

A

UpperBound - LowerBound

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Mean

A

Sum of values / number of values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Coding

Definition

A

A kind of transformation of data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Coding

General Form

A

y = (x-a) / b

x = original data or mean
y = new data or mean
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Q1

A

Lower Quartile

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Q2

A

Median

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Q3

A

Upper Quartile

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Interquartile Range

A

Q3 - Q1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Q1

List of Data

A

4 pots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Q1

Data in a Table

A

4 pots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Q1

Data in a Grouped Table

A

1/4 nth value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Q2

List of Data

A

4 pots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Q2

Data in a Table

A

4 pots
OR
n+1/2 th value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Q2

Data in a Grouped Table

A

n/2 th value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Q3

List of Data

A

4 pots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Q3

Data in a Table

A

4 pots

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Q3

Data in a Grouped Table

A

3/4n th value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Variance

Symbol

A

σ²

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Standard Deviation

Symbol

A

σ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Standard Deviation

Equation

A

√variance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Coding - Mean

±a

A

±a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Coding - Variance

±a

A

Not effected

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Coding - Standard Deviation

±a

A

Not effected

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Coding - Mean

xa

A

xa

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Coding - Variance

xa

32
Q

Coding - Standard Deviation

xa

33
Q

Coding - Mean

/a

34
Q

Coding - Variance

/a

35
Q

Coding - Standard Deviation

/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

‘

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

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)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions