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Fundamentals Of Mathematics > Data, Graphs and Statistics > Flashcards

Data, Graphs and Statistics Flashcards

1
Q

Probabilistic notation form?

A

P(event)

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2
Q

What does 0 mean in probability?

A

Impossible event

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3
Q

What does 1 mean in probably?

A

Certain event

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4
Q

What is theoretical probability?

A

Does not take take experimental data or bias into account

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5
Q

Formula for theoretical probability?

A

Number of ways even can occur
P(Y)= ————————————————
Total number of sample points

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6
Q

What is experimental probability?

A

Determined by performing an experiment and using data

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7
Q

Formula for experiment probability?

A

Number of ways event does occur
P(Z) = ———————————————-
Number of times experiment repeated

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8
Q

What is an independent event?

A

The results of one event does not affect the result of another

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9
Q

How to calculate the probability of multiple independent events?

A

Multiply together probabilities

May need to sum together and multiply more if we do not care about the order

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10
Q

How to use a tree diagram?

A

Multiply along the branches

Add up probabilities at end if needed

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11
Q

What is a depend event?

A

The outcome of the first event affects the second event

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12
Q

What is the expectation is probability?

A

The value we expect to happen

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13
Q

How to work out expectation?

A

Multiple each outcome by its probability

Add all these together

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14
Q

What is the expected frequency?

A

Used when expectation is not possible. E.g. cannot multiple green by 7

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15
Q

How to work out expected frequency?

A

Multiply the probability of the outcome by the amount of times we did the experiment

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16
Q

What is continues data?

A

Data can take any value, any number of decimals

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17
Q

Why is discrete data?

A

Only can be from a specific set of numbers, usually a whole number

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18
Q

What is categoric data?

A

Non-numerical categories. Can’t usually be ordered

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19
Q

What graph is used for categoric data?

A 
Bar chart (horizontal bars)
Pie chart
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20
Q

How to change percentage to degrees for a pie chart?

A

Multiply by 3.6

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21
Q

What type graph is used for discrete data?

A 
Bar chart (vertical bars)
Pie chart 
Histogram (useful for date with ranges) they represent frequency by the area of the bar rather than height
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22
Q

What type of graph is used for continuous data?

A 
Line graphs 
Scatter graphs (when both axis are continuous)
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23
Q

What do scatter graphs show?

A

Used to show whether there is a relationship between two sets of data

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24
Q

What is a negative correlation?

A

As one quantity increases the other decreases

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25
Q

What is a positive correlation?

A

As one quantity increases so does the other

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26
Q

What does no correlation mean?

A

No clear relationship between quantities

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27
Q

What type of graph has a best fit line?

A

Line graph NOT scatter graph

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28
Q

Reliability definition in regards to line graphs?

A

If all the points are close to the line of best fit with no anomalies

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29
Q

What does proportional mean in regards to line graphs?

A

Only if the line of best fit passes through the origin

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30
Q

What is the name of the equation that the graph represents?

A

The function

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31
Q

What is the domain?

A

The spread of the x values

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32
Q

What is the range?

A

The spread of y values

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33
Q

On a domain/range line what does a hallow or full circle mean?

A

Hallow means greater than or less than

Full means greater than, less than or equal to

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34
Q

How should decimals and significant figures be used in a table?

A

Going down a column where data is being measured there should always be the same number of decimal places
If data is being added or subtracted decimal places should also be maintained
If data is multiplied or divided then significant figures should be maintained rather than decimals

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35
Q

What is central tendency?

A

As we get more observations we tent towards a central value rather than an extreme value

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36
Q

How to calculate arithmetic mean?

A

Sum of all the values and divided by the number of values

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37
Q

Advantages of arithmetic mean?

A

Most efficient measure of central tendency

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38
Q

Disadvantages of arithmetic mean?

A

Can be substantially affected by large outliers

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39
Q

How to work out the mode?

A

The most common value

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40
Q

Advantages of the mode?

A

Can be used for categoric data. There can be multiple modes.

41
Q

Disadvantages of the mode?

A

Poor representation of actual most likely value as could easily be due to chance

42
Q

How to calculate the median?

A

The middle value once organised in numerical order. Or the average of the two middle terms.

43
Q

Advantages of the median?

A

Immune to outlier and skewed data, very good measure of central tendency

44
Q

Disadvantages of the mean?

A

Cannot be used for nominal data

45
Q

What is nominal data?

A

Categoric data that cannot be ordered

46
Q

What is ordinal data?

A

Categoric data that does have an order

47
Q

What is the range?

A

Subtract the lowest value from the highest value

48
Q

Disadvantages of the range?

A

Affected by outliers

49
Q

What is the interquartile range?

A

Splits data into four and finds the difference between end of 1st and end of 3rd quartiles

50
Q

Formula to work out 1st and 3rd quartile?

A

Q1=1/4(number of results+1)

Q3=3/4(number of results+1)

51
Q

Advantages of interquartile range?

A

Removes outliers

52
Q

How to correct quartiles figures when the formula produces a decimal?

A

Q1 .25 need to average the terms either side
Q1 .75 round the term up

Q3 .25 round the term down
Q3 .75 average the terms either side

53
Q

How to work out mean from a table of continuous data?

A

Find an average of each variable and times by frequency

Add all these together and divide by total frequency

54
Q

What is an uncertainty?

A

How far out a reading may be. E.g. +/- 0.01cm

55
Q

How to calculate absolute uncertainty in data with only one reading?

A

The value followed by the precision of instrument. This also works for repeat readings with the same values.

56
Q

How to calculate absolute uncertainty with repeat readings?

A

Multiply the range by 0.5

Value looking at +/- figure found from range

57
Q

How to calculate percentage uncertainty?

A

Absolute uncertainty
——————————— X 100
Value
Written as value with +/- percentage after (maximum % of 2 significant figures)

58
Q

How to combine uncertainties?

A

Add the percentage uncertainties together for multiplication and division
Add the absolute uncertainties for addition and subtraction

59
Q

How to calculate absolute uncertainty from percentage uncertainties?

A

Percentage uncertainty
————————————- x value
100
Never more decimal places than the value

60
Q

How to work out variance?

A

Standard deviation squared

61
Q

Difference between sample and population?

A

Population measures everyone/thing needed

Sample only measures a few out of a population

62
Q

How to work out sample standard deviation?

A 
First calculate mean 
Subtract the mean from every outcome and square the result 
Add all results together 
Then use formula:
S = √number found previously 
         ————————————-
          Number of results - 1
63
Q

What is normal distribution?

A

A probability distribution that suggests that most values cluster around middle of the range and taper off at each end
A bell shaped curve

64
Q

Features of the normal distribution?

A

Symmetric
Centred on mean
Continuous
All values are possible but those at extremes are unlikely

65
Q

How does normal distribution relate to standard deviation?

A

68% within 1 SD
95% within 2 SD
99.7% within 3 SD

66
Q

How to work out probability of something being ‘less than’ from normal distribution from standard deviation?

A

Value - mean
———————-
Standard deviation

Look at table and see what figure corresponds

67
Q

How to work out probability of something being ‘more than’ from normal distribution from standard deviation?

A

Calculate the ‘less than’ value and subtract this from 1

68
Q

How to find equation of straight line?

A

Work out relationship between x and y
Eg y =2x
Should always start with Y =
General equation of Y=Mx+c

69
Q

What describes the gradient?

A

Value in front of X from equation

70
Q

What does y=mx+c show?

A 
Equation of a straight line
Y= y axis
M=gradient 
X= x axis
C= constant (the Y intercept)
71
Q

How to find the gradient?

A 
Choose two coordinates on line
Use formula:
Y2-Y1
————
X2-X1
72
Q

The independent variable is usually the ….. axis?

A

X

73
Q

The dependent variable is usually the ….. axis?

A

Y

74
Q

What type of data is Poisson distribution used for?

A

Discrete

Usual rare events

75
Q

Lambda meaning?

A

Mean of all the expected number of results

76
Q

What type of date is binomial distribution used for?

A

Discrete

But only two options (success or failure)

77
Q

How to predict successes from binomial data?

A

Probability multiplied by number of experiments then look on probability graph

78
Q

Formula for probability from Poisson distribution?

A

??

79
Q

What is parametric data?

A

Date that is normally distributed e.g. height, weight

80
Q

What is a null hypothesis?

A

No significant correlation

81
Q

Hypothesis testing for parametric data?

A

Paired t-test
Unpaired t-test
Pearson correlation
ANOVA

82
Q

Hypothesis testing for non-parametric data?

A

Chi squared test
Mann-Whitney U test
Spearman correlation
Kruskal-Wallis

83
Q

What is a significance level?

A

How likely something is due to chance

P=

84
Q

What is the chi squared test used for?

A

Discrete data

Difference between what is expected and what is observed

85
Q

Chi-squared test procedure?

A

1) state null hypothesis
2) calculate expected frequency
3) use formula:
(Observed value - expected) (2)
X(2)= The sum of—————————————————-
Expected value
Easiest to calculate in a table
4)calculate degrees of freedom formula:
DF= number of classes-1
5) look up in table
6) accept or reject null hypothesis including significance level and degrees of freedom

86
Q

Degrees of freedom formula when working with distributions?

A

DF= number of classes- 1 - number of estimated parameters

Estimated parameters depends on whether binomial, Poisson or normal.

Binomial is 0
Poisson is 1
Normal is 2

87
Q

What is a tangent?

A

A straight line that to measure the gradient of a curved graph

88
Q

How to add an error bar to graph?

A

Add lines up/down/side to side of the uncertainty associated with value
Helps to add line of best fit, must pass through all error bars

89
Q

What is a worst best fit line?

A

As steep as it can go but still within all error bars and as shallow as it can go with another line

90
Q

Purpose of worse best fit line?

A

Can be used along side best fit line to see the range of gradient readings
Find different between best gradient and worts gradient to find uncertainty

91
Q

How to find the area under a graph?

A

Divide space to rectangles and triangles
Base x height for rectangles
1/2 base x height for triangles
Add together
If graph is curved
Count all squared, not including any less that half full

92
Q

What is the students T-test for?

A

When we have two samples to compare and then generate claims about the population

93
Q

Assumptions of students unpaired T-test?

A

Data normally distributed
Unpaired data
Unequally variance

94
Q

What is unpaired data?

A

Data from samples that do not impact on each other (different samples)

95
Q

What is paired data?

A

Data that does effect one another (same sample)

96
Q

How to use unpaired T-test?

A

1) find amount measured, mean and standard deviation for both groups
2) state null hypothesis
3) t= mean of first group- second group
———————————————————————
Variance of 1st group Variance of 2nd group
√(————————————) +(——————————-)
Number of obs. Number of obs.
4) ignore any negatives
5) calculate degrees of freedom
Obs. in group 1 + group 2 - 2
5) look up value in table
6) accept or reject null hypothesis at required significance level
7) state a conclusion

97
Q

How to use paired T-test?

A

1) find mean and stand deviation of differences
2) state null hypothesis
3) t=mean of differences √ number obs.
——————————————————————
Standard deviation of differences
4) ignore any negatives
5) calculate degrees of freedom
Number of obs. - 1
5) look up value in table
6) accept or reject null hypothesis at required significance level
7) state a conclusion

98
Q

Assumptions of students paired T-test?

A

Data normally distributed
Paired data
Unequally variance

Fundamentals Of Mathematics (2 decks)

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