Frequency Distribution Chart

Lets suppose we throw a dice 20 times and write down the number that is on the top.
{4,2,1,6,3,4,3,3,5,1,3,4,1,6,5,1,3,6,1,3}
We can construct a frequency table to show the results of this experiment.
The data in a frequency table can be quickly summarised by plotting a column chart.


Grouped Frequency Distribution

When you have a large amount of data you might want to group the data into categories (or intervals).
Lets consider that we only wanted to show 3 bars on our column chart. We could group the results in the following way

The data in this table can be quickly summarised by plotting a column chart.

Now this chart looks totally different to the first one and is very misleading.
This chart seems to indicate that the numbers that occurred the most were 4, 5 and 6.
To rectify this problem instead of plotting a column chart we can plot a histogram instead.


What is a Histogram ?

A histogram is an accurate way of representing a frequency distribution.
A histogram is a column chart with two important criteria:
0) There are no gaps between the columns.
1) The intervals must be the same width meaning the area underneath is proportional to the frequency.
Plotting a histogram of the grouped frequency distribution looks like this:

Notice that the y-axis has been changed to frequency density.




Cumulative Frequency Distribution

These are useful to show what proportion of a dataset lies above or below certain limits


Interval | Frequency | Cumulative f | Cumulative %


What percentage of this dataset scored over 41%


Percentiles are points on a frequency distribution below which a specified percentage of cases in the distribution fall
The 25th, 50th and 75th percentiles are referred to as quartiles
For more details about percentiles, please refer to Excel > Add-ins > Analysis ToolPak > Rank and Percentile


Frequency Polygon

A grouped frequency distribution can be displayed as a frequency polygon.
To construct a frequency polygon you must calculate the midpoint of each interval:

These midpoints are then joined together with straight lines to form a polygon.


Frequency Curve

When you have a large number of intervals the frequency polygon can be smoothed out to create a frequency curve.
It is often easier to see the shape of a distribution by using a frequency curver.

This distribution is slightly skewed.


Frequency Distribution Equation


When your data is in the form of a frequency distribution, the formula becomes:

and the alternative formula becomes:


When a frequency distribution is normally distributed we can find out the probability of a value by standardising the values.



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