Descriptive Statistics Calculator (Grouped Data)
Input Data
Enter class intervals (e.g., "1-7") and their frequencies.
How to Use This Calculator
1. Enter Your Grouped Data Intervals and Frequencies
The calculator requires you to define your class intervals and their corresponding frequencies.
- In the Interval input field, enter the lower and upper bounds separated by a hyphen (e.g., 1-7). Ensure your intervals are continuous (the upper bound of one class should match the lower bound of the next, e.g., 1-7, 7-13, 13-23).
- In the Frequency input field, enter the count of observations within that interval. This must be a non-negative number.
- Click the Add Interval Row (+) button to add more pairs of inputs if needed.
- Use the X button on the right of an input row to remove it.
2. Calculate Descriptive Statistics
Once all your intervals and frequencies are entered:
- Click the Calculate Statistics button.
- The calculator will process the data, perform calculations using the midpoint method, and display the results in the sections below:
- Calculation Table: Shows the Midpoint (M), Class Width (w), Density (d=f/w), Cumulative Frequency (F(x)), and intermediate steps ($f \cdot M$, $f \cdot M^2$).
- Summary Statistics: Provides the total frequency (n), Mean, Median, Mode (based on max density), Quartiles (Q1, Q3), IQR, and both Population and Sample Variance/Standard Deviation.
- Interpretations: Gives a quick explanation of what the main statistical measures mean in the context of your data.
3. Analyze the Density Histogram
The Data Visualization section presents a Density Histogram.
- In a density histogram, the bar height represents density (frequency / class width).
- The bar with the highest density (the tallest bar) identifies the Modal Class.
4. Use Advanced Features
The calculator provides two additional tools:
- Calculate Percentile Rank: Enter any value (e.g., 15.5) in the input box and click Calculate Percentile to find the estimated percentage of data points that fall below that specific value, using interpolation.
- Export Results: Use the buttons to Download Screenshot (.png) of the main content or Export Results as PDF (a full report including the table, stats, interpretations, and plot).
Example: Calculating Scores
Let's use a common scenario: test scores for 20 students, grouped into the following class intervals:
Interval (Score)
0-10 10-20 20-30 30-40Frequency (Students)
2 5 8 5To analyze this data, you would input the pairs (0-10, 2), (10-20, 5), (20-30, 8), and (30-40, 5) into the calculator's input fields and click Calculate Statistics.
Expected Insight: The modal class is 20-30, meaning most students scored in this range. The calculated mean score for the class is approximately 23.