Frequency Distribution
Calculate frequency distribution with frequency table, relative frequencies, mean, median, standard deviation, variance, skewness, and kurtosis from comma-separated data.
About This Calculator
This frequency distribution calculator creates a complete frequency table from your data, showing each unique value, its count, and relative frequency as a percentage. It also computes descriptive statistics including mean, median, mode, standard deviation, variance, skewness, and kurtosis. The frequency table helps you understand the pattern of your data at a glance, while the statistics provide a comprehensive numerical summary. Use this tool for statistical analysis in education, research, business analytics, and data science.
The calculator automatically sorts your data and counts how many times each value appears. The relative frequency column shows what proportion of the total each value represents, making it easy to compare distributions of different sizes. The bar chart visualizes the frequency of each value, while the cumulative frequency line chart shows running totals as you move from the smallest to the largest value — helping you quickly see how many data points fall at or below any given value.
The descriptive statistics give you a complete picture of your data's distribution. The mean is the arithmetic average, the median is the middle value, and the mode is the most frequently occurring value. Standard deviation and variance measure how spread out your data is from the mean. Skewness indicates whether your data is symmetric or skewed to one side, and kurtosis shows how prone your distribution is to outliers compared to a normal distribution. This tool is suitable for students, teachers, researchers, and professionals working with statistical data across any field.
Frequently Asked Questions
What is a frequency distribution?
A frequency distribution shows how often each unique value appears in a data set. It organizes data into a table with each value and its count, helping you understand which values are most and least common.
What is a relative frequency?
A relative frequency is the proportion of times a value occurs, calculated as the value's count divided by the total number of data points. It is often expressed as a percentage and helps compare distributions across different-sized data sets.
How do I read a frequency distribution table?
Each row shows a unique value from your data, its count (how many times it appears), and its relative frequency (percentage of total). The table is sorted by value for easy reference. The bar chart visualizes the distribution.
What is skewness?
Skewness measures the asymmetry of a data distribution. Positive skew means the tail is longer on the right (more extreme high values). Negative skew means the tail is longer on the left (more extreme low values). Zero indicates a symmetric distribution.
What is kurtosis?
Kurtosis measures the tailedness of a distribution. High kurtosis means more data in the tails (outliers are more likely). Low kurtosis means fewer outliers. A normal distribution has kurtosis of approximately 3 (excess kurtosis = 0).
How do I enter data for frequency distribution?
Enter your data as comma-separated numbers. For example: 1,2,2,3,3,3,4,4,5. The calculator will count the frequency of each unique value and compute all descriptive statistics automatically.
What is cumulative frequency?
Cumulative frequency is the running total of frequencies as you move from the smallest to the largest value. For each value, it shows how many data points are at or below that value. The cumulative frequency chart helps you quickly identify percentiles and understand the overall distribution shape.
How do you interpret skewness and kurtosis values?
Skewness near 0 means symmetric data. Positive skew (above 0) means the right tail is longer; negative skew means the left tail is longer. Kurtosis measures tail heaviness: excess kurtosis above 0 means heavier tails (more outliers), below 0 means lighter tails. A normal distribution has excess kurtosis of 0.