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Chapter 2 - Graphical and tabular descriptive techniques - Coggle Diagram
Chapter 2 - Graphical and tabular descriptive techniques
Descriptive statistics
Involves arranging, summarizing, and presenting data into useful information
Graphical techniques to describe nominal data
Summarize the data in a table that presents the categories
Relative frequency distribution lists the categories and the proportion with which each occurs
Only calculation is to count the frequency of each value of the variable
Use bar charts (gaps between) shows frequencies
Use pie charts (shows relative frequency)
Frequency polygon
Obtained by plotting the class frequency against the class midpoints as a line graph
Add a class below the first class and another above the last class
The relationship between 2 nominal variables
Cross-classification table
Describes the relationship between 2 nominal variables
Lists the frequency of each combination of the values of the 2 variables
Variable
Characteristic of the elements of a population or a sample
Data
The observed values of a variable
Relative frequency polygon
Relative frequency = number of observation / total number of observations
Obtained by plotting the relative frequency against the class midpoints as a line graph
When we are interested in the proportions between the classes
y-axis = proportion (percentage) of values in a given class
Ogive
Graphical representation of the cumulative relative frequencies
Created as follows
Calculate relative frequencies from the frequency distribution
For the first class, the cumulative relative frequency is simply the relative frequency
For the remaining classes, calculate relative frequency by adding the relative frequency to the class to the cumulative frequency of the previous class
Stem and leaf display
Can split @ the decimal point or at the tens
Must have a scale
Can compare to histograms by turning the display sideways
Split each observation into two parts
Constructing a histogram
Create a frequency distribution for the data
Always round down in surge's rule
Determine the class width
Range = largest value - smallest value
Range / number of classes = class width
Calculate the number of classes using Surge's rule:
c = 1 + 1.4 ln (n)
n -> number of observations in the sample
ln -> natural log
Logex = lnx
Count the number of observations in each class
Represent the distribution graphically
Graphical techniques to describe numerical data
Histograms are used
Used to summarize numerical data and used to calculate probabilities
Non-categorical
Types of calculations
Ordinal
Logical ordering / ranking
Values must represent the ranked order of the data
Calculations based on an ordering process are valid
Nominal
No logical ranking possible
Values are the arbitrary numbers that represent categories
Only calculations based on frequencies of occurrence are valid
Numerical
Values are real numbers
All calculations are valid
Representing time series data
Observations measured at the same point in time are called cross-sectional data
Observations measured at successive points in time are called time series data. Represented on a line chart
The relationship between 2 numerical variables
Scatter diagram / plot
Independent variables -> X-axis
Dependent variable -> Y-axis
Plots two variables against one another