General

Question 1

Sample percentile

Answer 1

Within a sample that has been ranked from least to greatest the 100p percentile of data is the value of data where

1. ) 100p percent of the data is equal to or less than the data value and
2. ) 100(1-p) percent are greater than or equal to it.

Question 2

A statistic

Answer 2

This is a numerical value that is derived from data.

Question 3

Bivariate Data Analysis

Answer 3

This is when you are investigating an IV and a DV and the relationship between IV and DV

Question 4

Box Plots

Answer 4

This is a plot that shows the extreme values, the first quartile, median, and third quartile.

Question 5

Central Tendency Measures

Answer 5

This is described by the mean, median, and mode of the dataset where the mean is influenced by the extreme values and median is independent

Question 6

Chubyshovs inequality

Answer 6

If we are trying to identify how much of a dataset lies between the values of x̄ +-ks where s = standard deviation and k = some number then

% min = 100(1- 1/(k²))

Question 7

Class Boundaries

Answer 7

These are the max/min of the class intervals. We use the left-end inclusion rule which says that the value to the left is included in the bin and the one in the right is not.

Question 8

Class intervals

Answer 8

These are the bins for grouping observations in a reasonable way.

Question 9

Closed Data

Answer 9

This is data that is of a fixed ratio where the maximum cannot exceed some value.

Examples include any cumulative data.

Question 10

Correlation Coefficient

Answer 10

r = [Σ (x_i - x̄)( y_i - ȳ)]/(n-1)s_xs_y = [Σ (x_i - x̄)( y_i - ȳ)]/[Σ (x_i - x̄)²( y_i - ȳ)²]^.5

This says that if we have a paired dataset such that x_i,y_i are the pairs and are described by their respective means such that y = mx + b then this statistic will indicate the linearity of the pairs of data

Question 11

Cumulative Frequency

Answer 11

This shows the bins as a function of an additive frequency.

These are also called Ogives

Question 12

Directional Data

Answer 12

This is data expressed in angles and can indicate how a vector is directed in space.

Question 13

Frequency Table

Answer 13

This is a table that displays the number of occurrences vs. a characteristic of the sample being investigated with relatively small and discrete values.

Question 14

Gini Coefficient

Answer 14

The gini coefficient (G) is the integral of the area between L(p) = 1 and the Lorenz Curve. It has a maximum value of .5 and a minimum value of 0

G=1-2B where B = area under Lorenze curve, L(p)

Question 15

Histograms

Answer 15

These are bar charts without spaces

Question 16

Image Processing

Answer 16

This is an increasingly important form of analysis that involves the changing of images from signals to visuals, enhancing the signal to noise ratio, extract features, and understand patterns.

Question 17

Inferential Statistics

Answer 17

This is the practice of using statistics to make inferences about a experiment or population

Question 18

Interval Data

Answer 18

These are data that are seperated by even values but they can be less than zero (temperature)

Question 19

Lorenz Curve

Answer 19

This is a cumulative curve showing the income distribution

Question 20

mean

Answer 20

x bar = Σx/n = Σ v*f/n

where v = bin value and f = frequency

Question 21

Mean influence by multiplication/addition

Answer 21

for some function y = ax+b

y bar = a x(bar) + b so the mean is affected by both multiplication and addition in a linear way

Question 22

Median

Answer 22

This is the middle value of a sample when data is arranged from least to greatest

If n is odd then the median value occurs at n = (n+1)/2

If n is even then the median is the average of (n/2)+1 and n/2

Question 23

Mode

Answer 23

This is the observed value that occurs most often within a dataset. If there are more than one values that occur the same number of times then there are modal values

Question 24

Nominal Data

Answer 24

This is data that is non-numerical in character (fossils, minerals, rocks…)

It is occasionally converted into binary (0=not present, 1 = present)

Question 25

Normal Data Set

Answer 25

This is a data set where mean=median=mode and where 68% of the data lies between x̄+-s 95% is within x̄ +-2s 99.7% is within x̄ +- 3s

Question 26

Ordinal Data

Answer 26

This is ranked data that can be numerical but the intervals separating the data is not equal. (Ex: Moh's scale of hardness). Values also cannot be negative

Question 27

Paired Data Sets

Answer 27

These are data sets that are trying to understand how one variable influences a different variable

Question 28

Population

Answer 28

This is the total collection of elements that we want to investigate. This is too large to investigate each of the contained elements.

Question 29

Probability Models

Answer 29

These are models that help us understand the validity of our conclusions by assigning probabilities of finding our results. It acts as the basis of statistical inference and if an inference cannot be checked using a probability model then we cannot conclude the inference is legitamate.

Question 30

r meaning

Answer 30

If the slope relating y and x is \<0 then r \<0 and vice versa. the absolute value of r indicates the linearity of the relationship If r is for (x, y) where w = a + bx and z = c + dy then r(x,y) = r(w,z)

Question 31

Ratio data

Answer 31

This is data that is greater than zero and on a scale where each interval is spaced evenly. Examples include weight or length

Question 32

Relative frequency

Answer 32

This is f/n where f is the number of occurrences for a given phenomena and n is the total number of phenomena investigated. The summation of f/n =1

Question 33

Sample 100p percentile

Answer 33

The data point equal to where less than 100\*p% of data lies. It includes that data point p=probability as a decimal

Question 34

Sample Variance

Answer 34

s²=Σ (x_i-x)² /(n-1) This fundamentally finds the average values of the squared difference of a data point to the mean (hypotenuse) It is squared to find the absolute value of the difference and not be influenced by negatives

Question 35

Samples

Answer 35

These are subgroups of populations which ideally represent the population

Question 36

Sampling Strategies (3 kinds for geology)

Answer 36

regular sampling is where sampling occurs in evenly distributed plots Uniform sampling occurs by taking random samples within a defined area clustered sampling takes samples from an outcrop or other area of limitted exposure

Question 37

Scatter diagrams

Answer 37

These are x vs y plots where y = DV

Question 38

signal processing

Answer 38

This includes all techniques for manipulating a signal to minimize the noise. They are most often used in combination with time series anlayses to make sense of things like geophysical data

Question 39

Spatial Analyses

Answer 39

This is a suite of techniques used to understand how observations relate to one another in 2 or 3 space.

Question 40

Spatial Data

Answer 40

This is data that is collected in either 2 or 3 space and represent the occurrence of something in space Ex: Spatial distribution of a tracer in water

Question 41

Spread influence

Answer 41

Central tendencies are influenced by addition/subtraction. Spread is not but multiplication changes spread by the constant squared

Question 42

Statistics

Answer 42

This is the art of learning from data and includes the collection, description, and inference of data

Question 43

Stem and leaf Plots

Answer 43

These are plots for small to medium datasets of data that have two parts which can be separated to make a stem and a leaf

Question 44

Time series Analysis

Answer 44

This is understooding data sequences as a function of time. It can also include periodic oscilatory data

Question 45

Univariate Data Analysis

Answer 45

This is reserved for data that is independent meaning that every outcome under analysis does not influence the other

Question 46

Ways to Display a frequency table

Answer 46

These can be displayed using line graphs, bar graphs, or frequency polygons

Question 47

Ways to show relative frequency

Answer 47

This can be shown on a table, line graph, bar chart, relative frequency polygon, or a pie chart.

Question 48

What is a common need for descriptive statistics?

Answer 48

We need to be able to display data in a way that makes it interpretable and meaningful. It should be intuitive.

Question 49

When are normal distributions most common?

Answer 49

These are most common in very large datasets or the conglomeration of datasets

Question 50

Finding a sample percentile

Answer 50

1. ) arrange data from least to greatest. n = number of data 2. ) find n\*p. The resultant value is the np'th smallest value which satisfies the 100p criterions. 3. ) IF np is not an integer then ROUND UP and that value is the 100p IF np is an integer then the 100p value is given by ((np)+(np+1))/2 This is like the median where if the median is an even number then you use the average of the n/2 and n/2+1 values

Question 51

Quartiles

Answer 51

These are the 25%th, 50%th, and 75%th values. You find what value of the data set meets these criteria by finding np where p = .25,.5,.75 and if np is whole use the average.

Question 52

Mean vs. Median when to use

Answer 52

Generally mean gives a better understanding of the dataset in terms of describing the data. The median should be used when probabilities are involved and/or the value is being used to understand the order of a group. Ex: Housing. The mean income would be best for determining what the average person in an area can spend on a home but if we want to design housing where we could expect 50% of the population could live (P(Affordable)=.5) then the median is more useful.

Question 53

Sample Space

Answer 53

S = sample space = all possible outcomes to some event or occurrence

Question 54

Subset

Answer 54

This is a specific outcome of the sample space S consisting of one or more outcomes that can be defined within one event.

Question 55

Intersection

Answer 55

This is the ∩ symbol that is used interchangeably with "and" To say we have two events, E ; F, which occur we could say EF, E∩F, or E and F This represents E and F must occur together and if E and F are mutually exclusive then EF = ϕ = null event

Question 56

Null event

Answer 56

ϕ = null event = the scenerio where the input situation cannot occur. This means that there is no way for the inputs to occur as described. Ex: if E and F are mutually exclusive then EF = ϕ because there are no parts of E and F that overlap

Question 57

Union

Answer 57

E U F = E or F which means that any outcomes within either subset or event E or F are valid.

Question 58

Compliment

Answer 58

If we have an event, E, within the sample space, S then E^c = compliment of E and includes everything that is not E

Question 59

Set Containment

Answer 59

If the occurrence of E means that F must have also occured then E is contained within F which is shown with a sideways U symbol

Question 60

Communitive law for union/intersection

Answer 60

E U F = F U E Event E or F = Event F or E EF=FE Event E and F = Events F and E

Question 61

Associative Law for Union and Intersection

Answer 61

(EUF)UG = EU(FUG) E or F or G = E or F or G EF(G) = (E)FG E and F and G = E and F and G

Question 62

Distributive law for intersection and union

Answer 62

(EUF)G = EGUFG Events (E or F) and G = Events E and G or F and G EFUG = (EUG)(FUG) Events E and F or G = (E or G) and (F or G)

Question 63

Demorgans Laws

Answer 63

(EUF)^C = E^CF^C E or F do not occur = E not occurring and F not occurring (EF)^C = E^C U F^C E and F not occurring = E not occurring or F not occurring

Question 64

Three axioms of Probability

Answer 64

1: 0 2: P(S) = 1 3: P(U_iⁿ E_i) =Σ_iⁿ P(E_i) = P(E₁) + P(E₂) +... +P(E_n) This is assuming that E_i and E_i+1 are mutually exclusive

Question 65

Sample spaces with equally likely outcomes

Answer 65

This refers to a sample space where each outcome has an equal probability of occurring, aka there is no **weight** to a particular outcome In this scenario P(E) = 1/N = p

Question 66

Theory of counting

Answer 66

This says that if we have a set of events that can occur inour sample space and each of these events creates a series of potential outcomes then the total number of outcomes is the product of the total number of secondary outcomes and the total number of first events In other terms if we have "r" experiments and each experiment has "n" outcomes then r\*n = total number of outcomes

Question 67

Permutations

Answer 67

This is a specific arrangement of a set of objects where the total number of permutations available to a subset of things is equal to n! where n is the total number of things in the subset

Question 68

number of unique groups in a set

Answer 68

If we have a sample of size = n and we want to know how many unique combinations of size r can be made from the elements of n this is = n!/[(n-r)!r!] This says that for a sample size=n that we can arrange "r" elements this many ways uniquely

Question 69

Combinations notation

Answer 69

The number of unique combinations of n within groups of size r (ⁿ_r) = n!/[(n-r)!r!] where r

Question 70

When is conditional probability particularly useful?

Answer 70

It is used when there is **limited information** within a problem (you are attempting to derive the probability of an event based on other events) or It is the easiest way to find the probability of a cause or input to an event with new information (backwards reasoning)

Question 71

P(E|F) = ?

Answer 71

P(E|F) = P(EF)/(P(F) Probability of E occurring given F has occurred = the probability E and F occur divided by the probability F occurs

Question 72

P(E|F^c) = ? (expand)

Answer 72

P(E|F^C) = P(EF^C)/P(F^c) This is says that the probability of E occurring given that F does NOT occur equals the probability of E occurring and F not occurring divided by the probability F does not occur.

Question 73

P(E) Expansion using compliments

Answer 73

P(E) = P(EF) + P(EF^C)) Probability of E = Prob of E and F + Probability of E and not F

Question 74

P(E) = ? as a weighted average

Answer 74

P(E) = P(E|F)P(F) + P(E|F^c)(1-P(F)) The P(E) = The weighted average of E occurring if F has occurred and if E occurs and F does not occur Where E occurs as the consequence of F.

Question 75

How to use the weighted probability of E?

Answer 75

If tasked with finding P(F|E) where E is the second event Then P(F|E) = P(FE)/(P(E) where P(FE) = P(F)P(E|F) and P(E) = P(F)P(E|F) + P(F^c)P(E|F^c)

Question 76

Independent events

Answer 76

If P(E|F) = P(E) then E and F are independent and E is not a function of event F and P(EFG)=P(E)P(F)P(G)