06 lecture

Presentation of data
Dr Md Anisur Rahman
Professor & Head of the Department
(Ophthalmology)
Dhaka Medical College, Dhaka
4/24/2021 1
anjumk38dmc@gmail.com

Different types of presentations
1) Table
2) Graph
3) Line Diagram
4) Scatter plots
5) Stem and leaf plots
6) Quartiles
7) Box-and-whisker plot
8) Pie chart
4/24/2021 2

4/24/2021 anjumk38dmc@gmail.com 3
1) TABLE

Some common recommendations to follow when
presenting data
 The presentation should be as simple as possible.
 Avoid the trap of adding too much information.
 A good rule of thumb is to only present one idea or to
have only one purpose for each graph or chart you
create.
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presenting data
 The presentation should be self-explanatory.
 A chart or graph is not serving its purpose if the
reader has to refer to the text in order to understand it.
 The title should be clear and concise indicating what?
When? Where? The data were obtained.
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presenting data
 Codes legends and labels should be clear and concise,
following standard formats if possible. (Legend is a broad
label for a group of objects that you would like to label, whereas label is
just for labeling specific elements.)
 The use of footnotes is advised to explain essential
features of the data that are critical for the correct
interpretation of the graph or chart.
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Construction of a Statistical Table
A statistical table has at least four major parts and some
other minor parts:
(1) The Title
(2) The Box Head (column captions)
(3) The Stub (row captions)
(4) The Body
(5) Prefatory Notes
(6) Foot Notes
(7) Source Notes

The general sketch of table indicating its
necessary parts is shown below:
• The title:
• Prefatory Notes
Box Head
Row caption Column caption
Sub Entries The body
Foot notes
Source notes

(1) The Title & (2) The Box Head (column
captions)
1) The title is the main heading written in capitals shown
at the top of the table. It must explain the contents of
the table and throw light on the table, as whole
different parts of the heading can be separated by
commas. There are no full stops in the little.
2) The vertical heading and subheading of the column
are called columns captions. The spaces where these
column headings are written is called the box head.
Only the first letter of the box head is in capital letters
and the remaining words must be written in lowercase.

(3) The Stub (row captions) & (4) The Body
3) The horizontal headings and sub heading of the row
are called row captions and the space where these rows
headings are written is called the stub.
4) This is the main part of the table which contains the
numerical information classified with respect to row and
column captions.

(5) Prefatory Notes & (6) Foot Notes
5) A statement given below the title and enclosed in
brackets usually describes the units of measurement and
is called the prefatory notes.
6) These appear immediately below the body of the
table providing additional explanation.

(7) Source Notes
The source notes are given at the end of the table
indicating the source the information has been taken
from. It includes the information about compiling
agency, publication, etc.

An ideal table has the following features
1) Limit your table to data that are relevant to the hypotheses
in the experiment.
2) Be certain that your table can stand alone without any
explanation.
3) Refer to all tables by numbers in your text, e.g., (in Arabic
numerals) Table 1, Table 2. Table 3...
4) Describe or discuss only the table's highlights in your text.
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An ideal table have the following features
5) Always give units of measurement in table headings.
6) Align decimal places.
7) Round numbers as much as possible. Try to round to
two decimal places unless more decimals are needed.
8) place the tables near the text that refers to them.
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9) Reasonable amount of data to be used, neither so small nor
to big data that the reader does not understand results,
10) Only include the necessary number of tables in your paper,
otherwise, it may be redundant or confusing to the reader.
11) Do not use tables if you only have two or fewer columns
and rows. In such cases, a textual description is enough.
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12) Organize your tables neatly so that the meaning of the
table is obvious at first glance.
13) Remember that too many rows or columns could make it
difficult for the reader to understand the data. You may
need to reduce the amount of data, or separate the data into
additional tables.
14) If you have identical columns or rows of data in two or
more tables, combine the tables.
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15)Provide column/row totals or other numerical
summaries that can make it easier to understand the
data.
16)Be consistent with your tabular presentation. Use
consistent table, title, and heading formats.
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Table, Frequency distribution
Table: 1. Rating of a hotel by its 20 boarders
Above average Above average Average
Average Above average Average
Above average Average Poor
Average Below average Above average
Poor Above average Above average
Below average Excellent Above average
Average Above average

Table: 2. Shows frequency distribution of rating of Hotel by 20 borders
Frequency Distribution
Rating Frequency Relative
frequency
Cumulative
frequency
Percent
frequency
Poor 2 10 2 0.10
Below
average
3 15 5 0.15
Average 5 25 10 0.25
Above
average
9 45 19 0.45
Excellent 1 5 20 0.05
20 100 1.00
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Tables: Relative frequency
So, Relative frequency =

The calculation for the first relative frequency is:
2/20 X 100 = 10
X 100
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Table: Cumulative frequency
The cumulative frequency is obtained by adding up
the frequencies as you go along, to give a 'running
total' “We could also call it a Running Total”
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Types of graph:
Graphs are a good means of describing, exploring or
summarizing numerical data because the use of a
visual image can simplify complex information and
help to highlight patterns and trends in the data.
1) Bar Chart
2) Histogram
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2) BAR-CHART

Bar charts
 Heights or lengths of the different bars are proportional
to the size of the category they represent.
 x-axis (the horizontal axis) represents the different
categories it has no scale.
 y-axis (the vertical axis) does have a scale and this
indicates the units of measurement.
 The bars can be drawn either vertically or horizontally
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3) HISTOGRAM

Histogram
Histogram is a graphical display of data using bars of
different heights
It is similar to a bar chart, but a histogram group
numbers into ranges. And you decide what ranges to
use.
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Difference between bar graph and histograph
Bar graph Histograph
1) Bar graphs are usually used
to display "categorical data"
1) Histograms on the other
hand are usually used to
present "continuous data"
2) Bars in bar graphs are
usually separated
2) In histograms the bars are
adjacent to each other.
3) Bar charts are used to
compare variables
3) histograms are used to show
distributions of variables
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How many groups should I have for a
histogram?
It is partly aesthetic judgment but, in general,
between 5 and 15, depending on the sample size,
gives a reasonable picture.
Try to keep the intervals (known also as "bin widths")
equal.
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4) STEM & LEAF

Stem and Leaf Plot
Stem and Leaf Plot is a special table where each
data value is split into a "stem" (the first digit or
digits) and a "leaf" (usually the last digit).
• The "stem" values are listed down, and the "leaf"
values go right (or left) from the stem values.
• The "stem" is used to group the scores and each "leaf"
shows the individual scores within each group.
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Stem and Leaf Plot
15, 16, 21, 23, 23, 26, 26, 30, 32, 41
Make a stem & leaf plot
Stem Leaf
• 1 5 6
• 2 1 3 3 6 6
• 3 0 2
• 4 1
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For example, a gynecologist in district general
hospital is investigating the Hb% of 24 women in
child bearing age (15 – 40 year). In a particular
village there are 24 women whose ages range from 15
to 40 year, and in a preliminary study the
gynecologist has found the following amounts of
Hb% given in Table 1 what is called an array
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1) 6.5, 2) 7.8, 3) 12.3, 4) 12.7,
5) 9.1, 6) 11.6, 7) 10.8, 8) 7.5,
9) 8.6, 10) 9.9, 11) 10.5, 12) 10.5,
13) 11.5, 14) 8.0, 15) 11. 0 16) 10.6,
17) 9.6, 18) 11, 3, 19) 6.4, 20) 7.5,
21) 10.9, 22) 9.3, 23) 8.7 24) 9.2.
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 We need to abbreviate the observations to two
significant digits. The digit to the left of the decimal
point is the "stem" and the digit to the right the "leaf".
We first write the stems in order down the page. We
then work along the data set, writing the leaves down
"as they come". Thus, for the first data point, we write a
5 opposite the 6 stem. These are as given in
4/24/2021 36

Figure: 3 Stem and leaf “as they come”
Stem Leaf
• 6 5, 4
• 7 8, 5, 5
• 8 6, 0, 7
• 9 1, 9, 6, 3, 2
• 10 8, 5, 5, 6, 9
• 11 6, 5, 0, 3
• 12 0, 7
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Figure: 4. Ordered stem and leaf plot
Stem Leaf
• 6 4, 5
• 7 5, 5, 8
• 8 0, 6, 7
• 9 1, 2, 3, 6, 9
• 10 5, 5, 6, 8, 9
• 11 0, 3, 5, 6,
• 12 0, 7
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5) QUARTILE

Quartile
• What is quartile?
• What is the relation of quartiles with median?
• Interquartile range
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What is quartile?
Quartile is a useful concept in statistics and is
conceptually similar to the median. The first quartile
is the data point at the 25th percentile, and the third
quartile is the data point at the 75th percentile. The
50th percentile is the median.
4/24/2021 41

To further see what quartiles do, the first quartile is at the
25th percentile. This means that 25% of the data is
smaller than the first quartile and 75% of the data is larger
than this. Similarly, in case of the third quartile, 25% of
the data is larger than it while 75% of it is smaller. For the
second quartile, which is nothing but the median, 50% or
half of the data is smaller while half of the data is larger
than this value.
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• What is the relation of quartiles with median? (14)
• We know that the median of a set of data separates the data into
two equal parts. Data can be further separated into quartiles. Quartiles
separate the original set of data into four equal parts. Each of these parts
contains one-fourth of the data. Quartiles are percentiles that divide the
data into fourths.
• The first quartile is the middle (the median) of the lower half of the
data. One-fourth of the data lies below the first quartile and three-fourths
lies above. (the 25th percentile)
•
• The second quartile is another name for the median of the entire set of
data. Median of data set = second quartile of data set. (the 50th percentile)
• The third quartile is the middle (the median) of the upper half of the
data. Three-fourths of the data lies below the third quartile and one-
fourth lies above. (the 75th percentile)
•
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The first quartile
is the middle (the
median) of the
lower half of the
data. One-fourth
of the data lies
below the first
quartile and
three-fourths lies
above. (the
25th percentile)
The second
quartile is
another name for
the median of the
entire set of data.
Median of data
set = second
quartile of data
set. (the
50th percentile
The third quartile
is the middle (the
median) of the
upper half of the
data. Three-
fourths of the
data lies below
the third quartile
and one-fourth
lies above. (the
75th percentile
4/24/2021 44

6) LINE DIAGRAM

Line Diagram
 What is a line graph?
 Example
 Why use a Line Graph?
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What is a line graph?
 A line chart or line graph is a type of chart which displays
information as a series of data points connected by straight
line segments. It is a basic type of chart common in many
fields.
 A line chart is often used to visualize a trend in data over
intervals of time – a time series – thus the line is often drawn
chronologically. In these cases they are known as run charts.
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• Which day did this person spend the most money? How do
we know? This person spent the most money on Thursday.
We know this because the graph is the highest on Thursday.
About how much money in total did this person spend on
Monday and Thursday? How do we know? This person
spent about Tk 500 on Monday and Thursday. We know this
because we looked at where the line was for Monday and
Thursday and added the two amounts.
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Why use a Line Graph?
A line graph has characteristics that make it useful for
some situations. We would use a line graph if:
• we have a function. Line graphs are good at showing
specific data values, meaning that if we have one
variable (x) we can easily find the other (y).
• We want to show trends. For example, how our
investments change over time or how food prices have
increased over time.
• We want to make predictions. A line graph can be
extrapolated beyond the data at hand. They enable we
to make predictions about the results of data.
4/24/2021 50

7) Scatter plot

Scatter plot
• What is a Scatter plot?
• How to construct/Read Scatter plot?
• Patterns of Data in Scatter plots
• Difference between line graph and scatter plot
4/24/2021 52

What is a Scatter plot?
A scatter plot is a graphic tool used to display the
relationship between two quantitative variables.
4/24/2021 53

Scatter plot
HEIGHT
(Inch)
WEIGHT
(Pounds)
67 155
72 220
77 240
74 195
89 175

How to Constructs/Read a Scatter plot?
A scatter plot consists of an X axis (the horizontal axis), a Y axis
(the vertical axis), and a series of dots. Each dot on the scatter
plot represents one observation from a data set. The position of
the dot on the scatter plot represents its X and Y values.
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 Pieces of data are collected and translated into points that,
when graphed, can be used to define the nature behind two
correlated variables (x and y).
• A line graph, on the other hand, displays the direct relationship
between the variables x and y.
4/24/2021 56

Box-and-whisker plot or box plot
• A five-number summary of a data set
Box-and-whisker plot or box plot is a diagram
based on the five-number summary of a data set. It is used
is in non-parametric data. Before have a clear idea of
Box-and-whisker plot we have to know what are the five-
number summaries of a data set? The five-numbers are:
i. Minimum number
ii. Maximum number
iii. Median (or second quartile)
iv. The first quartile, and
v. The third quartile.
4/24/2021 57

How to construct a box-and-whisker plot?
Construct a box-and-whisker plot for the following data:
The data:
Math test scores: 80, 75, 90, 95, 65, 65, 80, 85, 70, and 100
Step 1: Arrange them in ascending order:
65, 65, 70, 75, 80, 80, 85, 90, 95, and 100
Step: 2. . Identify the median (the value in the middle)
65, 65, 70, 75, 80, 80, 85, 90, 95, and 100
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Step: 3. Identify the lower quartile – (median of the lower half)
And the upper quartile – (median of the upper half)
65, 65, 70, 75, 80, 80, 85, 90, 95, 100
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median of the
lower half
Median
median of the
upper half

Step: 4. Draw a box – from the lower to the upper quartile.
Step: 5. Draw a line in the box to show the median.
Step: 6. Draw the whisker – to the minimum and maximum.
60 70 80 90 100

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