# Frequency Distribution: Graphs or Diagrams

### Histogram

The
histogram is used to present data that has been arranged in a frequency
distribution table into a graph. The main use of a histogram is to show the
general form of data distribution and to give a visual impression about the
concentration of most observations. Presentation of data in graphs is often
more effective than presenting in tables. For example extreme values or
outlier data can be easily identified if the data is presented in a graph. In
addition, the concentration and distribution of data around the concentration
can also be observed visually.

To make it easier to understand the explanation, we need a new table, i.e.

We arrange the table by adding a midpoint column as listed in the table above.

How to determine the midpoint at a class interval is to add up the lower class limit and the upper class limit and then divide 2 (two). For example the midpoint for the first class interval is (16 + 27) / 2 = 21.5; and so on for the middle class in another class.

After the midpoints from all class intervals have been obtained, we then arrange them in the form of a histogram. How to make a histogram are as follows:

- Create a cross axis with f as the ordinate (y axis) and X as abscissa (x axis) and specify the appropriate scale.
- Starting with the first class, draw a beam as high as the frequency stated by the class and through the midpoint as its axis, the width of the class matches the width of the class. And so on until the last class. It should be noted that, for discrete data one beam must be drawn separately from the next beam. For continuous data between two beams there is no distance, because it is a continuation of the other. For example discrete data histograms from the following table:

### Stem and Leaf Diagram

Stem
and leaf diagrams are another alternative that can be used to present and
simplify data. The output is almost the same as the histogram and frequency
distribution, the difference is that in the bar and leaf diagram the visualized
data is the actual data value (not data that has been grouped into class
intervals).

Some
of the uses of stem and leaf diagrams include the following:

- To show the range of data, which is the difference between the largest and smallest data.
- To show data distribution.
- In general, to indicate the location of concentration and data distribution.
- To indicate whether or not there is outliers or outlier data, that is extreme data whose value is very large or very small.

With a stem and leaf diagram, each observation value is separated into the next digit into a leaf from this diagram. For example the data in the following table below,

Insurance Statistics Final Exam Value Data from 50 Students,

The values of these observations are all worth tens. In this case tens numbers can be used as head digits and unit numbers are used as tail digits. Because the observation value ranges between 35 and 92, we will have seven bars (digit heads) that reflect dozens of numbers, namely: 3, 4, 5, 6, 7, 8, 9. These seven bars function the same as intervals class in the frequency distribution table. The tail digit of the observation value is then written on the relevant line. The first observation is 77, then the number 7 (digit digit) is written on the first leaf close to the stem value 7 (digit of the head). And so on until the value of the last observation. As presented below,

Stem and Leaf Diagrams Final Score for Insurance Statistics Subjects from 50 Students.

Steam-and-leaf of data N = 50

Leaf Unit = 0.1

3 5

4 025789

5 3356667888999

6 000112567889

7 0111333347889

8 0578

9 2

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