The document discusses different methods for presenting data graphically and numerically, including frequency distributions, histograms, and frequency polygons. It provides details on how to construct each type of graph or table. A frequency distribution displays the number of observations within intervals and can be shown graphically or in a table. A histogram uses rectangular bars to show the frequency distribution where the area of each bar is proportional to the frequency. A frequency polygon connects the midpoints of the bars on a histogram to form a polygonal shape.

1. Data Presentation using
Descriptive Graphs/Tables

2. OPENING PRAYER

3. A. FRENQUENCY DISTRIBUTION
A frequency distribution is a representation, either in a
graphical or tabular format, that displays the number of observations
within a given interval. The interval size depends on the data being
analyzed and the goals of the analyst. The intervals must
be mutually exclusive and exhaustive. Frequency distributions are
typically used within a statistical context. Generally, frequency
distribution can be associated with the charting of a normal
distribution.

4. Frequency distribution in statistics is a representation that
displays the number of observations within a given interval.
The representation of a frequency distribution can be graphical
or tabular so that it is easier to understand.
Frequency distributions are particularly useful for normal
distributions, which show the observations of probabilities
divided among standard deviations.
In finance, traders use frequency distributions to take note of price
action and identify trends

5. RANGE - The difference between the largest value
and smallest value in the data set.
Example:
34, 68, 84. 76, 61
61, 85, 54, 44,
70, 72, 83, 61
Range: 85-34= 51

6. CLASSES AND CLASS INTERVALS
RANGE: LENGTH OF CLASS
BN-SN INTERVAL (h):
RANGE
No. of classes

7. IQ SCORES Frequency
81-90 IIIII-IIIII-IIIII-IIII
91-100 IIIII-IIIII-IIIII-IIII
101-110 IIIII-IIIII-IIII
111-120 IIIII-IIIII-IIIII
121-130 IIIII-IIIII-IIIII-IIIII
131-140 IIIII-IIIII-III
Range: Length of classes:
140-81= 59 59/6= 9. – or 10
TOTAL: 100

8. B. HISTOGRAM/BAR GRAPH
A two dimensional graphical representation of a continuous
frequency distribution is called a histogram.
In histogram, the bars are placed continuously side by side with no
gap between adjacent bars.
That is, in histogram rectangles are erected on the class intervals
of the distribution. The areas of rectangle are proportional to the
frequencies.

9. You need to follow the below steps to construct a histogram.
1. Begin by marking the class intervals on the X-axis and
frequencies on the Y-axis.
2. The scales for both the axes have to be the same.
3. Class intervals need to be exclusive.
4. Draw rectangles with bases as class intervals and
corresponding frequencies as heights.

10. 5. A rectangle is built on each class interval since the class
limits are marked on the horizontal axis, and the
frequencies are indicated on the vertical axis.
6. The height of each rectangle is proportional to the
corresponding class frequency if the intervals are equal.
7. The area of every individual rectangle is proportional to
the corresponding class frequency if the intervals are
unequal.

11. The histogram graph is used under certain conditions. They are:
1. The data should be numerical.
2. A histogram is used to check the shape of the data
distribution.
3. Used to check whether the process changes from one period
to another.
4. Used to determine whether the output is different when it
involves two or more processes.
5. Used to analyse whether the given process meets the
customer requirements.

12. Difference Between Bar Graph and Histogram

15. Types of Histogram
The histogram can be classified into different types based on the
frequency distribution of the data. There are different types of
distributions, such as normal distribution, skewed distribution, bimodal
distribution, multimodal distribution, comb distribution, edge peak
distribution, dog food distribution, heart cut distribution, and so on. The
histogram can be used to represent these different types of distributions.
The different types of a histogram are:
- Uniform histogram - Bimodal histogram
- Probability histogram - Symmetric histogram

20. FOR EXAMPLE:
Draw a histogram for the following table which represent the
marks obtained by 100 students in an examination:
Solution :
The class intervals are all equal with length of 10 marks.
Let us denote these class intervals along the X-axis.
Denote the number of students along the Y-axis, with
appropriate scale.

22. C. FREQUENCY POLYGON
A frequency polygon is a graphical form of
representation of data. It is used to depict the shape of the
data and to depict trends. It is usually drawn with the help of
a histogram but can be drawn without it as well. A histogram
is a series of rectangular bars with no space between them
and is used to represent frequency distributions.

23. Steps to Draw a Frequency Polygon
 Mark the class intervals for each class on the horizontal axis. We
will plot the frequency on the vertical axis.
 Calculate the classmark for each class interval. The formula for
class mark is:
Classmark = (Upper limit + Lower limit) / 2
 Mark all the class marks on the horizontal axis. It is also known as
the mid-value of every class.
 Corresponding to each class mark, plot the frequency as given to
you. The height always depicts the frequency. Make sure that the
frequency is plotted against the class mark and not the upper or
lower limit of any class.

24. This resulting curve is called the frequency polygon.
Join all the plotted points using a line segment. The curve
obtained will be kinked.
This resulting curve is called the frequency polygon.
Note that the above method is used to draw a frequency polygon
without drawing a histogram. You can also draw a histogram first
by drawing rectangular bars against the given class intervals. After
this, you must join the midpoints of the bars to obtain the frequency
polygon. Remember that the bars will have no spaces between
them in a histogram.

25. Question 1: Construct a frequency polygon
using the data given below:

26. Answer: We first need to calculate the cumulate frequency
from the frequency given.

27. We now start by plotting the class marks such as 54.5, 64.5, 74.5 and
so on till 94.5. Note that we will also plot the previous and next class
marks to start and end the polygon, i.e. we plot 44.5 and 104.5 as
well.
Then, the frequencies corresponding to the class marks are plotted
against each class mark. Like you can see below, this makes sense
as the frequency for class marks 44.5 and 104.5 are zero and
touching the x-axis. These plot points are used only to give a closed
shape to the polygon. The polygon looks like this:

29. C. MASTER DATA SHEET
Master coding sheet serves as an important
tool in data analysis
The data collected should be coded in order
to do statistical analysis.
Code the demographic values.
Scoring for research tool should be entered in
the master coding sheet.

32. https://www.investopedia.com/terms/f/frequencydistribution.asp
https://www.onlinemath4all.com/graphical-representation-of-a-frequency-
distribution.html#:~:text=a%20frequency%20distribution%22-
,Histogram,class%20intervals%20of%20the%20dist ribution.
https://www.sciencedirect.com/topics/mathematics/frequency-
polygon#:~:text=A%20frequency%20polygon%20is%20a,3.3
https://www.toppr.com/guides/maths/statistics/frequency-polygon/
• https://www.spss-tutorials.com/frequency-distribution-what-is-it/
https://byjus.com/maths/histogram/