PDF Analysing data (M248)

Analysing Data by Descriptive Statistics and
Graphical Appraise
TMA 01
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Question 1
a) Japanese black pine tree seedlings
i. Side-by-side box plot and Interval plots are two suitable graphical displays for
studying the distribution of the heights of the trees. Box plots are good for
comparison of height of trees for the four years (categorical variable). Interval
plot represents the continuous data with respect to the categorical variables and
the graphical display can be interpreted easily.
ii. Number of trees alive, is a discrete variable and each stage is also a categorical
variable. Hence, a bar diagram could easily represent the data for easy stage to
stage comparison for number of trees alive.
iii. Two way scatter plot would be a suitable graphical display to study the heights of
the trees depend on their ages, as both heights and age are continuous variables.
Marginal plot could be the alternative plot for representing graphically the
dependence of heights of the trees on their ages. This type of plots not only
presents the relation between the variables, but also presents in the distribution of
each of the variables separately in the plot itself.
b) Depth of snow at different locations on an Antarctic ice:
i. Minitab’s default frequency histogram for Depth is provided below (Lee, Lee,
Chang, & Tai, 2016).
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16
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10
8
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4
2
0
Depth
Frequency
Histogram of Depth
Figure 1: Default Histogram of Snow Height
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The distribution of the heights of 114 places of snow depth is roughly symmetric and is bimodal.
There seems to be outlier snow depths above 80 cm of snow depth. Average snow height is
observed to be around 40 cm of snow height. Huge fluctuations are noticed in the distributions
and the average deviation was believed to be somewhere between 20 cm to 25 cm.
ii. Minitab’s frequency histogram for Depth with suggested cut points is provided
below.
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25
20
15
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Depth
Frequency
Histogram of Depth
Figure 2: Histogram with Specific Cut Points
The random fluctuations in the default histogram have been smoothened by the choice of the
particular cut points. The bimodal and symmetric nature of the histogram is clearly visible in the
current diagram. Considering the physical phenomenon that has been plotted in the histogram,
wider bin size is expected to reduce the noise in the data due to low density of the data points.
iii. Unit-area histogram for Depth
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