Frequency Table
Data that comes as a table: each value with how often it occurs, or classes such as 40–50 with a count. Get the mean, median, mode, standard deviation and quartiles without typing out every single value.
3, 6. Class intervals: the class, then its count, e.g. 40-50, 3; a value on a boundary belongs to the higher class. For classes the calculator uses the class midpoints, so the results are estimates.What is a Frequency Table?
A frequency table lists each value once, with its frequency f: how many times it occurs. The mean is then a weighted average, Σf·x / Σf, and the same goes for the standard deviation.
With grouped data you only know how many values fall in each class, not the values themselves. The usual approach is to treat every value as if it sat at the class midpoint. The median and quartiles are estimated by assuming the values are spread evenly through their class.
Bar Chart
nYour Frequency Table
with cumulative counts| Value | Count f | Cumulative | % | Cumulative % |
|---|
Worked Techniques
Multiply each value by its count, add up, and divide by the total number of values.
Use the midpoint of each class as its value. The result is an estimate: the true values inside a class are not known.
Find the class that holds the middle value. L is its lower boundary, F the count below it, f its own count and w its width.
Sources & Verification
- D. C. Montgomery & G. C. Runger, Applied Statistics and Probability for Engineers, 6th ed., Wiley, 2013 — Ch. 6 (Descriptive Statistics).