The document discusses various graphical methods for presenting data, including histograms, polygons, pie charts, ogives, and stem-and-leaf plots. Histograms display the frequency distribution of data using bars of varying heights. Polygons connect the midpoints of histogram bars with straight lines. Pie charts represent proportions using circular slices. Ogives show cumulative frequencies with class limits on the x-axis and cumulative counts on the y-axis. Stem-and-leaf plots break values into "stems" and "leaves" for an organized display of the raw data. Examples are provided for constructing each type of graph using sample data sets.

1. Graphical
Presentation
of Data
Tar. Rangga Masyhuri Nuur
D-IV LLU 27
16072010021

2. Histogram
1

3. A graphical representation of a dataset that
displays the frequency distribution of the data.
● It consists of a series of bars, where the height of each
bar corresponds to the frequency (or count) of values
within a particular interval or "bin" of the data. The width
of the bins can be uniform or vary in size depending on
the range of the data and the desired level of granularity
in the histogram.
● commonly used in data analysis and statistics to visualize
the distribution of numerical data and identify patterns,
trends, and outliers in the data.
Histogram

4. Example of Using Histogram
A dataset of exam scores from a class of 30 students, and we want to create a histogram to visualize the
distribution of the scores. Here's an example of how we could do that:
1. First, we would determine the range of the scores and decide on the size of the bins. Let's say the scores
range from 60 to 100, and we decide to use bins of size 5 (i.e., each bin will represent a range of 5 points).
2. Next, we would count the number of scores that fall into each bin. For example, we might find that there are
2 scores between 60-64, 5 scores between 65-69, 8 scores between 70-74, and so on.
3. Then, we would create a histogram by plotting a bar for each bin, where the height of the bar corresponds to
the number of scores in that bin. The bars would be adjacent to each other, with no gap between them, to
indicate that the bins are contiguous.
4. Finally, we might add labels to the axes and a title to the histogram to provide context and clarify what the
histogram represents.
The resulting histogram would provide a visual representation of the distribution of exam scores, showing how
many students scored in each range and how the scores are distributed across the range. This could help us
identify any patterns, such as whether the scores are skewed to one side or evenly distributed, and make
inferences about the performance of the class as a whole.

5. Polygon
2

6. A graph that represents the frequency distribution of a
dataset. It is created by joining the midpoints of the
tops of the bars in a histogram with straight line
segments. The resulting shape resembles a polygon,
hence the name.
● A polygon graph can be used to visualize the shape of
a distribution, including any skewness or bimodality.
It can also be used to compare the distributions of two
or more datasets. By superimposing the polygons on
the same graph, it is easy to visually compare the
shapes of the distributions and identify any
differences or similarities.
● In summary, a polygon in statistics refers to a graph
that represents the frequency distribution of a dataset
by joining the midpoints of the tops of the bars in a
histogram with straight line segments.
Polygon

7. Example of Using Polygon
Suppose we have data on the ages of a group of people, and we want to visualize the distribution of
ages using a polygon graph. Here are the steps we could follow:
1. We start by creating a histogram of the ages. Let's say we decide to use bins of width 5,
starting from age 20 and ending at age 70. We count the number of people in each bin and plot
a bar for each bin on the horizontal axis.
2. Next, we calculate the midpoints of the tops of each bar in the histogram. For example, if the
bar for ages 20-24 has a height of 10, we would plot a point at the midpoint of this bar, which
would be at age 22.5 and height 10.
3. We then connect the midpoints with straight line segments to create a polygon graph. The
resulting shape will show the frequency distribution of the ages in the dataset.
4. Finally, we might label the axes and add a title to the graph to make it clear what it represents.
The resulting polygon graph would allow us to see the shape of the distribution of ages, including
any skewness or bimodality, and compare the distribution to other datasets or theoretical
distributions.

8. Pie Chart
3

9. Pie Chart
A circular statistical chart that is used to represent
numerical data as proportional slices or wedges of a
circular pie.
• The size of each slice corresponds to the proportion of
the data that it represents.
• Typically used to show the relative proportions of
different categories within a dataset or to compare the
sizes of different parts of a whole.
Pie charts are divided into sectors or wedges that
correspond to each category of data being represented.
The angle of each sector is proportional to the
percentage or fraction of the data that belongs to that
category. The total angle of a pie chart is 360 degrees,
representing the entire dataset. Pie charts often include a
legend that identifies the categories represented by each
slice or wedge.

10. Pie Chart
Pie charts are commonly used in business,
marketing, and other fields where it is important to
present data in a clear and visually appealing way.
However, they can also be criticized for being
difficult to interpret accurately when there are too
many categories or when the differences between
categories are small.

11. Example of Using Pie Chart
Suppose we have data on the sales of a company in a given year. The sales are divided into
four categories: product A, product B, product C, and product D. Here are the steps we
could follow to create a pie chart to visualize the sales data:
1. We start by calculating the total sales for the year. Let's say the total sales were Rp.
1,000,000.
2. Next, we calculate the proportion of the total sales that corresponds to each product
category. Let's say the sales for each product category were:
Product A: Rp. 300,000
Product B: Rp. 200,000
Product C: Rp. 250,000
Product D: Rp. 250,000

12. Example of Using Pie Chart
The proportions of the total sales for each product would be:
Product A: 30%
Product B: 20%
Product C: 25%
Product D: 25%
3. We then draw a circle and divide it into sectors or wedges that correspond to each
product category. The size of each sector would be proportional to the percentage of
the total sales that it represents.
4. We label each sector with the name of the product and the percentage of the total
sales that it represents. We might also include a legend that identifies each product
category.
The resulting pie chart would allow us to see the relative proportions of each product
category and compare them to each other. We could quickly see that product A represents
the largest proportion of sales, while products B, C, and D have similar proportions.

13. Ogive
4

14. A graph used in statistics to represent cumulative frequency
distributions. The cumulative frequency of a dataset is the
total frequency up to a certain point or value. The ogive
displays the cumulative frequencies of a dataset by plotting
the cumulative frequency against the upper boundary of
each class interval.
Ogive

15. The ogive graph is created by plotting points on a graph with
the upper limits of the class intervals on the x-axis and the
cumulative frequencies on the y-axis. The points are then
connected by straight lines to create a continuous curve. The
resulting graph shows the cumulative frequency distribution
of the dataset and allows us to visualize the shape and
spread of the data.
Ogives can be useful in identifying the median, quartiles, and
other percentiles of a dataset. They can also be used to
compare the cumulative frequency distributions of two or
more datasets.
Ogive

16. Example of Using Ogive
Suppose we have data on the number of books read by a group of students over the course of a school year.
The data is divided into class intervals of 0-4, 5-9, 10-14, and so on. Here are the steps we could follow to
create an ogive graph to visualize the cumulative frequency distribution of the data:
1. We start by creating a frequency distribution table that shows the number of students who read a certain
number of books in each class interval. Let's say the table looks like this:
Class Interval Frequency
0-4 10
5-9 20
10-14 30
15-19 25
20-24 15

17. Example of Using Ogive
2. Next, we calculate the cumulative frequency for each class interval by adding the frequencies of all the
previous intervals. The cumulative frequency table would look like this:
3. We then plot the cumulative frequencies on the y-axis and the upper boundary of each class interval on the
x-axis. For example, for the class interval 0-4, we would plot a point at x=4 and y=10.
4. We connect the points by straight lines to create the ogive graph.
The resulting ogive graph would allow us to visualize the cumulative frequency distribution of the data and see
how many students read a certain number of books or more over the course of the school year. We could also
use the graph to identify the median, quartiles, and other percentiles of the data.
Class Interval Frequency
Cumulative
Frequency
0-4 10 10
5-9 20 30
10-14 30 60
15-19 25 85
20-24 15 100

18. Stem and Leaf
5

19. Stem and Leaf
A graphical representation of a data set that displays
the individual data values in a way that allows us to
see the distribution of the data.
In a stem and leaf plot, each data point is broken into
two parts: the stem and the leaf. The stem represents
the leading digit or digits of the data value, while the
leaf represents the trailing digit(s). The stems are
listed in a vertical column and the leaves are listed to
the right of each stem in a horizontal row.

20. Example of Using Stem and Leaf
For example, if we have the data set {12, 13, 14, 23, 25, 27}, we can create a stem and leaf plot as
follows:
In this plot, the stems are 1 and 2, and the leaves for each stem are listed to the right. The stem 1 has
leaves 2, 3, and 4, while the stem 2 has leaves 3, 5, and 7.
Stem and leaf plots are useful for visualizing the distribution of the data and identifying patterns,
clusters, or outliers in the data set. They are particularly useful for small to medium-sized data sets
where the individual values can be easily displayed.
Stem Leaf
1 2 3 4
2 3 5 7

21. Thanks!