Frequency Distribution Calculator

A frequency distribution organizes raw data points into distinct classes or categories, displaying the count of observations occurring within each interval. The fundamental components involve determining the range (difference between maximum and minimum values), selecting an appropriate group size (class width), and tallying the occurrences (frequency, $f$). Cumulative frequency is calculated by sequentially adding the frequencies of each successive group. To find the mean ($ar{x}$) of a grouped frequency distribution, we multiply the midpoint ($m$) of each class by its corresponding frequency, sum those products, and divide by the total sample size ($N$): $\bar{x} = \frac{\sum (f \cdot m)}{N}$.

Imagine you have a dataset of 10 test scores: 55, 62, 65, 70, 72, 75, 78, 80, 85, and 92. You want to organize this data using a group size (class width) of 10, starting from a baseline value of 50. First, we establish our class intervals: 50–59, 60–69, 70–79, 80–89, and 90–99. Next, we count how many scores fall into each bin: 50–59 has 1 score (55); 60–69 has 2 scores (62, 65); 70–79 has 4 scores (70, 72, 75, 78); 80–89 has 2 scores (80, 85); and 90–99 has 1 score (92). The cumulative frequency for the third interval (70–79) is 1 + 2 + 4 = 7, meaning 7 out of 10 students scored below 80.

When selecting your group size, aim for between 5 and 15 intervals; too few intervals hide important details, while too many create unnecessary clutter. Ensure that your class intervals are mutually exclusive and of equal width so that no data point can fall into multiple categories and no bias is introduced into graphical representations like histograms.