Organising Data
Organising Data
Graphical presentation of quantitative data
(also available on elearn.mzuni.ac.mw)
Organising Data
Histogram
Histogram
A histogram displays the classes (ideally the class boundaries)
on the horizontal axis and frequencies on the vertical axis
Each class has a bar whose height equals the frequency of the
class
Unlike in a bar chart the bars in a histogram are not disjoint.
Bars for two consecutive classes meet at the common
boundary shared by the classes
Ideal for presenting grouped frequency distributions
Organising Data
Histogram
Frequency distribution for quantitative data
Example of a grouped frequency distribution
Let’s consider constructing a histogram for the following frequency
distribution
Weight Frequency (number of students)
118 - 127 3
128 - 137 6
138 - 147 14
148 - 157 9
158 - 167 5
168 - 177 3
Organising Data
Histogram
Histogram
Histogram
We need the class boundaries which (from the previous
lecture) are 117.5, 127.5, 137.5, 147.5, 157.5, 167.5, 177.5
Now for each class we construct a vertical bar with its feet at
the class boundaries and its height equal to the frequency of
the class
This yields the following histogram
Organising Data
Histogram
Histogram
Histogram
Organising Data
Frequency polygon
Frequency polygon
A frequency polygon is constructed by plotting the class
midpoints (on the horizontal axis) against class frequencies
(on the vertical axis). The plots are the connected using
straight lines. If the plots are connected using a smooth
curve, then we end up with a frequency curve.
Recall that the class mid point of a given class is given by
lcl + ucl
2
We now construct a frequency polygon for the frequency
distribution below (considered earlier)
Organising Data
Frequency polygon
Frequency polygon
Example - frequency polygon
Weight Frequency (number of students)
118 - 127 3
128 - 137 6
138 - 147 14
148 - 157 9
158 - 167 5
168 - 177 3
Organising Data
Frequency polygon
Frequency polygon
Example - frequency polygon
Since we plot class midpoints against frequencies, we need to
compute the class midpoints for the frequency distribution
lcl + ucl
using the formula . The computations are presented
2
in the following table
Weight class midpoint Frequency
118 - 127 118+1272 = 122.5 3
128+137
128 - 137 2 = 132.5 6
138 - 147 138+1472 = 142.5 14
148 - 157 148+1572 = 152.5 9
158 - 167 158+1672 = 162.5 5
168+177
168 - 177 2 = 172.5 3
Organising Data
Frequency polygon
Frequency polygon
Frequency polygon
So we plot 122.5 on the horizontal axis against 3 on the
vertical axis, 132.5 on the horizontal axis is plottd against 6
on the vertical axis, 142.5 on the horizontal axis is plotted
against 14 on the vertical axis etc
Joining the plots using straight lines we obtain the following
frequency polygon;
Organising Data
Frequency polygon
Frequency polygon
Frequency polygon
Organising Data
Frequency polygon
Frequency polygon
Frequency polygon
Note that the frequency polygon is sort of “hanging in the
air” as it is not touching the horizontal axis.
Now to prevent the polygon from “hanging in the air”, you
introduce two extra classes; one at the beginning of the
distribution and another at the end of the distribution, both
with frequency 0.
Then plot their class midpoints against zero.
In the example above the two extra classes would be 108 - 117
and 178 - 187 with midpoints 112.5 and 182.5 respectively.
Organising Data
Cumulative Frequency poygon
Cumulative frequency polygon
A cumulative frequency polygon is a graph constructed by
plotting the class boundaries (on the horizontal axis) against
their corresponding cumulative frequencies (on the vertical
axis). The plots are joined by straight lines.
If the plots are joined using a smooth curve then you end up
with a cumulative frequency curve.
A cumulative frequency polygon or cumulative frequency
curve is also referred to as an ogive
You can also obtain an ogive by plotting the class boundaries
against the cumulative relative frequencies or cumulative
percentages
In the following example we construct a cumulative frequency
polygon for the frequency distribution above.
Organising Data
Cumulative Frequency poygon
Cumulative Frequency poygon
Cumulative frequency polygon
Recall that the following is the frequency distribution that we
are considering;
Weight Frequency (number of students)
118 - 127 3
128 - 137 6
138 - 147 14
148 - 157 9
158 - 167 5
168 - 177 3
Organising Data
Cumulative Frequency poygon
Cumulative Frequency poygon
Cumulative frequency polygon
Since we plot the class boundaries against the corresponding
cumulative frequencies, we need the cumulative frequency
distribution for the frequency distribution above, and the
cumulative frequency distribution in question is the following;
Class boundary Cumulative Frequency
117.5 0
127.5 3
137.5 9
147.5 23
157.5 32
167.5 37
177.5 40
Organising Data
Cumulative Frequency poygon
Cumulative Frequency poygon
Cumulative frequency polygon
Thus 117.5 on the horizontal axis will plotted against 0 on the
vertical axis, 127.5 on the horizontal axis will be plotted
against 3 on the vertical axis, 137.5 on the horizontal axis will
be plotted against 9 on the vertical axis etc
Next,we join the plots using straight lines and this yields the
following;
Organising Data
Cumulative Frequency poygon
Cumulative frequency polygon
Cumulative frequency polygon (ogive)
Organising Data
Reading assignment
Reading assignment
From the text book obtained by your class rep, read, learn and
understand how to construct a stem and leaf diagram.
