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`"Frequency"_"X" = "Count of " X " within sub-range"_i, " where i = 1 .. Bins"`

Enter a value for all fields

The **Frequency Distribution** calculator bins and counts numeric values from a set (X) and creates a frequency distribution matrix of that data.

**INSTRUCTIONS:** Enter the following:

- (
**X**) - This is a string of numeric data listed as comma-separated values - (
**Low**) - This is the lower boundary of the lowest bin. - (
**High**) - This is the upper boundary of the greatest bin. - (
**B**) - This is the number of bins into which to split the range

**Frequency Distribution:** The calculator return listing where each row represents a bin, and were the first number in each row is the bottom of the bin, the second number it the top of the bin, and the third number is the number of observations in set X that fell into that bin.

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.

X may be input as integers or real numbers or a mix of the two. Values in `X` must fall between the Low and High Boundaries inclusive. In other words:`"Low" <= X_i <= "High"

This vCalc equation 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:

- `"value"_X >= "bin's lower boundary AND value" < "bin's upper boundary"`

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:

- there were no values in the frequency bin whose bounds are 0 to 20
- there was one value in the bin whose range is from 20 to 40
- there was one value in the bin whose range is from 40 to 60
- there were seven values in the bin whose range is from 60 to 80
- there were 10 values in the bin whose range is from 80 to 100.

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.

**Observational Stats**: This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns. This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.**Frequency Distribution**: This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins. It then computes how many of the observations are in each of the bins between the high and low values designated.**Paired Sample t-test**: This computes the various parameters associated with the Paired Sample t-test.**ANOVA (one way)**: The is one way analysis of variance**(χ**This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.^{2}) Chi-Square Test:**Linear Regression**: This computes the regression line (least-squares) through a set of X and Y observations. It also computes the regression coefficient (r).**y = a + bx**: This is linear equation used with Linear Regression to predict values of Y.**Wilcoxon Signed Rank Test**: This provides the Wilcoxon statistics and critical value for two groups of numeric observations based on an alpha value and whether it's a one or two tailed test.- Slope-Intercept form of a Line based on two points.
- Slope between two points
- Range value based on the slope-intercept formula of a line and a value of the domain.
- Compute the Probability between z SCORES
- College Level Statistics Calculator (Stat Calc).
- Count of Observations in a Set - this is the number (n) of values in a set.
- Minimum Value in a Set - this is the minimum observed value
- Maximum Value in a Set- this is the maximum value in the set.
- Numeric Sort (up and down) - this returns a comma separated list of the observations in ascending or descending order.
- Create a random subset of the a list of numeric values
- Random number from a range you specify
- Frequency distribution of data.
- Σx - this is the sum of the values in a set.
- Σx² - this is the sum of the squared values
- (Σx)² - this is the square of the summed values.
- Mean
- Median - the middle ordered value
- Mode - the most recurring observation
- Mid Point in a Set - this is the mid point of the observation range.
- Range in a Set - this is the difference between the max and the min.
- Population Variance of the values
- Population standard deviation of the values
- Sample Variance of the values
- Sample Standard Deviation of the values
- Compute the z SCORE based on the mean and standard deviation
- Compute the z SCORE in a set of observations
- Compute the percentile of a single observation (y) in a set (X)
- SDOM - standard deviation of mean
- Percent Relative Standard Deviation