The Frequency Distribution calculator takes an input set of data, `X`, and creates a frequency distribution matrix of that data.
5 bin Frequency Distribution for set:
(98, 90, 92,78, 76, 26, 58, 60, 66, 75,
95, 95, 100, 78, 85, 66, 100, 89, 80)
INSTRUCTIONS: Enter the following:
Frequency Distribution: The calculator returns a count of all of the values of X in evenly spaced bins between the low and high values set by the user.
The user specifies the boundaries of the possible range of `X` and the number of bins into which the user wishes to bin the frequencies. vCalc then splits the range into equal sub-ranges or "bins". The counts of data values falling between the upper and lower boundary of each bin is then displayed as the frequency distribution.
This calculator computes the possible range of `X` defined by the input Low and High values.
"Range"_X = "High" - "Low"`
The equation then splits the range up into the number of equal increments or frequency bins which is defined by the "Bins" input.
The frequency distribution is then computed and the count of data values which fall in each of the sub-range Bins is determined.
A count for each data value is put into the bin if the data value meets the condition:
A count is added to the top bin if: `"value" = "High"`, the top of the range
There are 19 student in the 1st year Algebra Class. They have just taken a test and we will check out how their test scores fall within the possible test score range.
The test score range is Low = 0 to High = 100.
Copy/Paste the following data set into the equation and set Bins to 5:
98, 90, 92,78, 76, 26, 58, 60, 66, 75, 95, 95, 100, 78, 85, 66, 100, 89, 80
We get back a frequency distribution from vCalc that looks like the example image at the right:
This frequency distribution tells us that:
The frequency distribution tells us about how the data in a data set is distributed. In an easy-to-grasp visual the frequency distribution tells us that a sampled set of data has tendencies to fall in one part or another of a data range.
Our example of test data shows a grouping of most of the values at the top end of the range. Of course, this is what we expect to see in a class room led by a competent instructor. The instructor's goal is to help the student maximize their learning experience and the students strive to get high grades, so you would expect the frequency distribution to be skewed toward the upper bins of the grading scale.
If the scores resulting from a test were skewed toward the lower bins, the teacher would know the student were not grasping the lessons for some reason. From the frequency distribution chart for combined scores over a period of time, the instructor could gain some understanding of how significant the lack of understanding might be.
Frequency distributions with real-world data tend to follow a pattern referred to as a "normal distribution". When frequency distributions are applied to unbiased, real world data, you will often see a "normal distribution" or bell-shaped curve. This reflects the tendency of data in nature to cluster around the center of the possible range and taper off in the direction of both the upper and lower bounds.
The data example at the right exhibits a somewhat normalized distribution with the center frequency bin showing 7 data values and the data values in the upper and lower bins showing fewer values as we move toward the Lowest and Highest bound of the data range for `X`.
The figure at the left represents a normal distribution. You can see the obvious bell shape of the frequency values represented by the yellow columns.