Posted by: tonyteaching | June 9, 2009

Graph, Central Tendency, & Variability

Why do we need Graph or Table?

to present the information

  • more concise (detail, as short as possible but clear)
  • more descriptive
  • more attractive



1. LINE Chart  linechart

fits for presenting

  • Trend
  • Value for Continuous data (both vertical & horizontal variables, e.g. temperature in each time in a day)

2. BAR Chart  barchart

fits for presenting

  • Comparison in values

3. PIE Chart  piechart

fits for presenting

  • Composition


Another special Graph is

HISTOGRAMS  histogram

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



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)


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)



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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