Here are the steps to construct a frequency distribution and histogram for the given data: 1. Group the data into class intervals of width 10. The class intervals are: 40-49, 50-59, 60-69, 70-79, 80-89, 90-99, 100-109. 2. Count the frequency of observations in each class interval. 3. The frequency distribution is: Class interval: Frequency 40-49: 1 50-59: 2 60-69: 4 70-79: 6 80-89: 8 90-99: 3 100-109: 1 4. Construct a histogram with the class intervals on the x

1. Data organization &
presentation

2. • Once data has been collected, it has to be organized and
classified in such a way that it becomes easily readable and
interpretable.
• Measurements that have not been organized, summarized or
otherwise manipulated are called raw data.
• First step in organizing data is the preparation of an ordered
array.
• An ordered array is listing the values in order of magnitude from
the smallest value to the largest value.
• Summarizing qualitative data is very straight forward, the main
task is being to count the number of observation in each
category. These counts are called frequencies.

3. • Data can be presented in one of the three ways
• As text: It is the main method of conveying information and it is
used to explain results and trends and provide contextual
information.
• In tabular form: It conveys information by converting words and
numbers into rows and columns. It is easier to see patterns and
relationship.
• In graphical form: Graphs simplify complex information by using
images and emphasizing data patterns or trends and are useful
for summarizing, explaining or exploring quantitative data.

4. Tabular forms
• Array: An array is a matrix or rows and columns of numbers
which have been arranged in some orders.
• Simple tables: A table needs a heading and names of variables
involved.

5. • Compound tables: It is an extension of simple table where more
than one variable is used. We may also refer a compound table
as a cross-tabulation or contingency table depending on the
context in which it is used.
• Bivariate table: When two variables are presented in one
table.
• Multivariate table: When more than two variables are used in
one table.
Age
group yr
Male Female
Illiterate Literate Illiterate literate
<40
≥ 40
Total

6. • Frequency distribution of grouped data: To group a set of
observations first to select a set contiguous, non overlapping
intervals such that each value in the set of observations can be
placed in one and only one of the interval. These intervals are
known as class interval.
• Width of class interval should be of same width. This width may
be determined by dividing the range R by k, the number of class
interval.

7. • Rule of thumb: Class interval width of 5 units, 10 units.
Following points should be kept in mind for classification
1. The classes should be clearly defined and should not lead to
any ambiguity
2. The classes should be exhaustive and each of the given
values should be included in one of the classes
3. The classes should be mutually exclusive and non
overlapping
4. The classes preferably of equal width
5. The number of classes should neither be too large or too
small
6. There should no gaps between groups

8. Inclusive & Exclusive Class Interval
1. When the lower and upper class limit is included, then it is an
Inclusive Class Interval. For example 21- 25, 26-30. Usually in
discrete variable, this type of class interval is used.
2. When the lower limit is included, but the upper limit is
excluded, then it is an Exclusive Class Interval. For example,
20 - 25, 25- 30. In case of continuous variable, exclusive class
interval is used.

9. Drawing/ Graphical presentation
For quantitative data, common graphs are
1. Histogram
2. Frequency polygon
3. Frequency curve
4. Line chart/graph
5. Cumulative frequency polygon or Ogive
6. Scatter plot
7. Stem and leaf
8. Box and Whiskers diagram

10. • The common diagrams for qualitative variable are:
1. Bar diagram
i. Simple Bar diagram
ii. Multiple bar
iii. Proportional/ component bar
1. Pie chart
2. Pictogram
3. Spot map

11. Simple bar diagram
• Only one variable is presented in a simple bar diagram.
• Steps of drawing a bar diagram
• Construct scale by a horizontal line which is known as x-axis
and a vertical line which is y – axis.
• Place categories of the variable on the x-axis and y-axis
represents the frequency or percentage of the categories.
• Width of the bars should be equal.
• Gap between the bars should also be equal.

12. Component bar diagram
• Categories of a variable forms a bar which constitutes 100%.
• Scale the y-axis from 0% to 100%.
• A bar on x-axis should be as tall as 100%.
• The bar is constituted as per proportion of the categories.

14. Pie diagram
• A pie diagram is similar to component bar diagram.
• In pie diagram all the components adds up to 360 degree as a
circle consists of 3600.
• Steps
• Multiply percentage of a category
by 3.6 and get the angle
for that category
• Draw a circle.
• Place the categories in the circle
• according to the calculated angles.

15. Pictogram
Spot map

16. Histogram
• A histogram is used to display the continuous variable.
• A histogram is a set of vertical bars whose areas are
proportional to the frequencies of the classes that they
represent.
• In a histogram the variables are taken on x-axis and the
frequencies are repented on y-axis.
• Each class is then represented by a distance on the scale that
is proportional to the class interval.
• Unlike the bar charts, there are no gaps between successive
rectangles of a histogram.
• A histogram is two-dimensional, here both length and width are
important.

18. Histogram with unequal class interval
• In this situation, correction must be made and it can be done by
finding the frequency density of each class.
• The frequency density will be the actual heights of the
rectangles since the areas of the rectangles should be
proportional to the frequencies.
• Frequency density =
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝐶𝑙𝑎𝑠𝑠 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙

20. Frequency polygon

21. Line chart/graph
• A line chart shows the frequencies for different values of a
variable. Successive points are joined by means of line
segments so that a glance at the graph tells the distribution of
the variable.
• Simple line chart: When values of one variable is presented.
Trends can be determined.
• Multiple line chart: More than one variables are presented
here. Comparison between variables and also trends can be
understood.

22. Simple line graph Multiple line graph

23. Cumulative frequency polygons or Ogives
• It is generated when cumulative frequencies are plotted on real
limits of classes of a distribution.
• Cumulative frequency means that the frequencies of classes
are accumulated over the entire distribution.
• Two types of cumulative frequency
1. ‘Less than’ cumulative frequency: It is the total number of
observations in the entire distribution, which is less than or equal to
the real upper limit of the class.
2. ‘More than’ cumulative frequency: It is the total number of
observations in the entire distribution, which is more than or equal to
the real lower limit of the class.

25. Scatter plot
• This type of diagram is used to investigate the relationship
between two continuous variables.
• In such a relationship, there is usually an independent variable
and a dependent variable.
• It is a prerequisite diagram in correlation and regression
analysis.

27. Stem and leaf
• Stem and leaf is also known as stemplot used to represent raw
data, that is individual observation without loss of information.
• The leaves of the diagram are the last digits of the observation
while the stems are the remaining part of the value.
• Suppose, the value 117, here ‘11’ is the stem and ‘7’ is the leaf.

28. Raw data

29. Box and Whiskers diagram
• Box and whiskers diagram is usually known as boxplots,
specially designed to display the dispersion and skewness of
the distribution.
• The figure consists of a box in the middle from which two lines
(whiskers) extends toward minimum and maximum values of
the distribution.
• A box plot is drawn according to 5 descriptive statistics
• Minimum value
• Upper quartile
• Median
• Lower quartile
• Maximum value

31. Exercise
65 91 85 76 85 87 79 93
82 75 100 70 88 78 83 59
87 69 89 54 74 89 83 80
94 67 77 92 82 70 94 84
96 98 46 70 90 96 88 72
1. Construct a frequency distribution
2. Construct a corresponding histogram