Why do we need Graph or Table?
to present the information
- more concise (detail, as short as possible but clear)
- more descriptive
- more attractive
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GRAPH
fits for presenting
- Trend
- Value for Continuous data (both vertical & horizontal variables, e.g. temperature in each time in a day)
fits for presenting
- Comparison in values
fits for presenting
- Composition
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Another special Graph is
Histogram is just like Bar Chart but the Vertical variable (Y) is Frequency of data and the Horisontal variable (X) is Continuous data (usually the continuous data are grouped into class intervals — the large of interval is depent on the actual data & the research interest). So there is no gap space among the groups.
Why do we need Histogram?
- When we want to know the number/frequency of a continuous variable
- then we want to know the shape of the frequency distribution (uni-modal, bi-modal, multi-modal) and the symmetry (skewed data)
- When we want to know how much are the data spread out
- To check/make sure there is no Outlier data/not
Ideally (e.g. no extreme data), the shape of the frequency distribution is Normal (‘Bell curve’)
In a Normal curve, the mean ~ median ~ mode (similar)
so all of them can represent the common data
Otherwise,
if the Mean < Median < Mode –> the shape of the frequency distribution is Negatively skewed (Left skewed)
if the Mean > Median > Mode –> the shape of the frequency distribution is Positively skewed (Right skewed)
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Additionally, the the shape of the frequency distribution is uni-modal = 1 curve containing only one mode
but some data can be bi-modal (2 curve/peaks containing two modes) or even multi-modal (more than 2 curve/peaks and 2 modes)
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VARIABILITY or Dispersion
Two parameters for measuring the variability or dispersion of data
1. Range: the difference between the largest and the smallest value of the data
Range of the data one of the data variability
2. Standard Deviation : the average’ distance of each data from the mean
Standard Deviation ~ Variability (the larger the SD, the greater the variability of the data)
Symbol of Standard Deviation for a Sample is s, where for population is sigma
Standar Deviation for a Sample
s: standar deviation for a sample (look for Sample, the n is minus 1!)
X : each data
M : mean
n : number of data
Standard Deviasion for a Population
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