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1.20.1.15 - Data Interpretations - Coggle Diagram
1.20.1.15 - Data Interpretations
types of data
nominal/categorical data
mutually exclusive but not ordered
no quantative value
no measure of difference
can be listed with numbers
numbers are meaningless and cannot be used for computation
e.g. hair colour/gender
ordinal data
there are catgories
e.g. how satisfied are you with your day (1-5)
one category can be higher than another
no quantitive measures of distance/difference
order is important
interval data
e.g. location, temperature, date
we know the order and the exact difference between values
the zero value is not meaningful and is set arbitratily
zero does not correspond to the absence of data
intervals do not have lower or upper bounds
ratio
we know the order and exact differences between values
there is a true zero
e.g. weight, height, duration
zero - absence of
comparison is meaningful
constructing graphs and interpreting data
bar chart
nominal
must be organised into categories
pie chart
nominal or ordinal
not practical where there are more than five/six values for a variable
histogram
ordinal
interval
ratio
most often used with ratio or interval level data
pie charts
a graph showing the difference in frequencies or percentages among categories of a nominal or ordinal variable
circular statistical graphic
divided into slices to illustrate numerical proportion
area is proportional to quanitity
bar charts
shows categorical data
data is shown as bars
height/length is proportional to the values they represent
possible to make comparisons to visualise the differences in data
constructed by plotting the categories on axes
categories are displayed on one axis and the values on the other
histograms
graph displaying frequencies or percentages among categories of an interval-ratio variable
displayed as contiguous bars
width is proportional to the width of the category
possible to visualise the differences in the frequencies or percentages among categories
to constuct:
create bins
bins are a series of intervals of the entire range of values of the variable under consideration
the bins are adjacent to each other and are usually of equal size
consecutive and non-overlapping
histogram vs bar chart
histograms are for continuous data
bar chaerts are for discrete categories of data
scatter plots for correlation
displays the strength and direction of a relationship
between two quantitive variables
correlation coefficient (-1 to 1) displays the strength of relationship
populations and samples
population - all of the elements from a set of data
sample - one of more observations collected from the populations
describing a sample
central tendency
measures that seek to identify the typical value in a set of data
dispersion
measures that seek to quantify the degree of scatter of data around a measure of central tendency
central tendency
interval
mean
ordinal
median
ratio
mean
nominal
mode
interquartile range
distance between the 25th percentile and the 75th percentile
useful for highly skewed data
useful for ranked data
measure of spread
dispersion
interval
standard deviation (IQR if skewed)
ordinal
IQR
ratio
standard deviation (IQR is skewed)
nominal
none
rates
measurement/time
e.g. m/s, mph
rates can change b changing time or measurement within the fixed time