Statistics 1 Flashcards
0
Q
Class Midpoint
A
(UpperBound + LowerBound) / 2
1
Q
Steps of Modelling a Mathematical Problem
A
- Observe a real world problem
- Devise a mathematical model
- Use the model to make predictions for the real world
- Experimental data is collected from the real world
- Compare predicted and observed outcomes
- Statistical tests are used to assess the model
- Mathematical model is improved and refined
2
Q
Class Width
A
UpperBound - LowerBound
3
Q
Mean
A
Sum of values / number of values
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
5
Q
Coding
Definition
A
A kind of transformation of data
6
Q
Coding
General Form
A
y = (x-a) / b
x = original data or mean y = new data or mean
7
Q
Q1
A
Lower Quartile
8
Q
Q2
A
Median
9
Q
Q3
A
Upper Quartile
10
Q
Interquartile Range
A
Q3 - Q1
12
Q
Q1
List of Data
A
4 pots
13
Q
Q1
Data in a Table
A
4 pots
14
Q
Q1
Data in a Grouped Table
A
1/4 nth value
15
Q
Q2
List of Data
A
4 pots
16
Q
Q2
Data in a Table
A
4 pots
OR
n+1/2 th value
17
Q
Q2
Data in a Grouped Table
A
n/2 th value
18
Q
Q3
List of Data
A
4 pots
19
Q
Q3
Data in a Table
A
4 pots
20
Q
Q3
Data in a Grouped Table
A
3/4n th value
21
Q
Variance
Symbol
A
σ²
22
Q
Standard Deviation
Symbol
A
σ
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
24
Q
Standard Deviation
Equation
A
√variance
25
Variance
| Equation (data in a table)
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
26
Variance
| Equation (data in a grouped table)
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
27
Coding - Mean
| ±a
±a
28
Coding - Variance
| ±a
Not effected
29
Coding - Standard Deviation
| ±a
Not effected
30
Coding - Mean
| xa
xa
31
Coding - Variance
| xa
xa²
32
Coding - Standard Deviation
| xa
xa
33
Coding - Mean
| /a
/a
34
Coding - Variance
| /a
/a²
35
Coding - Standard Deviation
| /a
/a
36
Frequency Density
| Formula
Frequency Density = Frequency / ClassWidth
37
Negative Skew
Q2 - Q1 > Q3 - Q2
mode > median > mean
38
Positive Skew
Q2 - Q1 < Q3 - Q2
mode < median < mean
39
Symmetrical Skew
Q2 - Q1 = Q3 - Q2
mode = median = mean
40
Outlier
An extreme value
Greater than Q3 + (1.5 x IQR)
OR
Les than Q1 - (1.5 x IQR)
41
Experiment
| Definition
A repeatable process that gives rise to a number of outcomes
42
Event
| Definition
A collection or set of one or more outcomes
43
Sample Space
| Definition
The set of all possible outcomes of an experiment
44
Probability
| '
Not
45
Probability
| U
Union
AND
OR
46
Probability
| n
Intersection
| AND
47
Addition Rule
P(AnB) = P(A) + P(B) - P(AUB)
48
Multiplication Rule
P(A|B) = P(AnB) / P(B)
49
Complimentary Probability
P('A) = 1 - P(A)
50
Mutually Exclusive Events
| Definition
Events have no outcomes in common
51
Mutually Exclusive Events
| Formulae
P(AUB) = P(A) + P(B)
P(A|B) = 0
P(AnB) = 0
52
Independent Events
| Definition
Events that have no effect on each other are independent
53
Independent Events
| Formulae
P(AnB) = P(A) x P(B)
P(A|B) = P(A)
54
Bivariate Data
| Definition
Data that comes in pairs
55
Variability of Bivariate Data
| Sxx
Sxx = Ex² - (Ex)²/n
56
Variability of Bivariate Data
| Syy
Syy = Ey² - (Ey)²/n
57
Variability of Bivariate Data
| Sxy
Sxy = Exy - (ExEy)/n
58
Product Moment Correlation Coefficient
| Symbol
r
59
Product Moment Correlation Coefficient
| Formula
r = Sxy / √(SxxSyy)
60
Product Moment Correlation Coefficient
| r = 1
perfect positive linear correlation
61
Product Moment Correlation Coefficient
| r = -1
perfect negative linear correlation
62
Product Moment Correlation Coefficient
| r = 0
no linear correlation
63
Regression Line
| Definition
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
Regression Line
| Formula
y = a + bx
```
a = y - bx
b = Sxy / Sxx
```
65
Interpolation
| Definiton
Estimating the value of the dependent variable within the range of data
66
Extrapolation
| Definition
Estimating the value of he dependent variable outside of the range of data
This can be unreliable
67
Probability Distribution
| Definition
A table showing the probability associated with each outcome of an experiment
68
Discrete Random Variables
| Expectation
E(X) = E x P(X=x)
69
Discrete Random Variables
| Variance
Var(X) = E(X²) - (E(X))² = E x² P(X=x) - (E(X))²
70
Discrete Random Variables
| Coding - Expectation
E(aX+b) = aE(X) + b
71
Discrete Random Variables
| Coding - Variance
Var(aX+b) = a² Var(X)
72
Discrete Uniform Distribution
Each outcome has the same probability
P(X=x) = 1/n
73
Discrete Uniform Distribution
| Expectation
E(X) = (n+1) / 2
74
Discrete Uniform Distribution
| Variance
Var(X) = (n+1)(n-1) / 12
75
Conditions for a Discrete Uniform Distribution
A discrete random variable X is defined over a set of n distinct values
Each value is equally likely
76
Standard Normal Distribution
Z~N (0,1²)
