Formula used
Pearson first coefficient: Skewness = (Mean − Mode) ÷ Standard Deviation.
Pearson second coefficient: Skewness = 3 × (Mean − Median) ÷ Standard Deviation.
Grouped median: Median = L + ((N ÷ 2 − CF) ÷ f) × h.
Grouped mode: Mode = L + ((fm − f1) ÷ (2fm − f1 − f2)) × h.
Here, L is the lower class limit, N is total frequency, CF is cumulative frequency before the class, f is class frequency, h is class width, fm is modal frequency, f1 is previous frequency, and f2 is next frequency.
How to use this calculator
Select the input mode that matches your data. Use raw values for a simple list. Use frequency rows when each value has a count. Use grouped rows for class intervals. Use summary statistics when mean, median, mode, and standard deviation are already known.
Choose population deviation when your data is complete. Choose sample deviation when your data represents a larger group. Select a mode option if the data has no clear mode. Press calculate. The result appears above the form. Use the export buttons to save the report.
Understanding Pearson Skewness
Pearson coefficient of skewness gives a quick view of shape. It compares the center of a data set with its spread. A balanced data set has a value near zero. A right tailed set has a positive value. A left tailed set has a negative value. The method is useful because it uses familiar statistics. You only need mean, median, mode, and standard deviation.
Why this calculator helps
Manual work can be slow when values are repeated, grouped, or entered as a long list. This calculator supports raw values, value frequency pairs, grouped classes, and summary inputs. It also lets you select population or sample standard deviation. That choice matters when the data is a full population or only a sample from a larger group.
Choosing the right Pearson method
Pearson’s first coefficient uses mode. It works well when a clear mode exists. Some data sets have no repeated value. Some have many modes. In those cases, the second coefficient is often safer. Pearson’s second coefficient uses median. It is common in classroom statistics and descriptive reports.
Reading the output
The sign shows direction. Positive skew means high values pull the mean above the center. Negative skew means low values pull the mean below the center. The size shows strength. Small values near zero suggest weak skew. Larger absolute values show stronger asymmetry. Always check the data table before making a final judgment.
Good data habits
Clean data gives better results. Remove text, blank entries, and impossible values. Use the same unit for every observation. For frequency data, make sure each frequency is positive. For grouped data, enter lower limit, upper limit, and frequency. Wider classes can reduce precision, because grouped calculations use midpoints and class formulas. Save the CSV or PDF report when you need a record for assignments, audits, or team review. Use the result as a guide, not as a final story. Skewness does not show every pattern. Two data sets can share one coefficient and still look different. Review histograms, outliers, and sample size when possible. For business, science, or school work, report the method used. This keeps your conclusion clear and repeatable for readers and future checks during later reviews as well.
FAQs
What is Pearson coefficient of skewness?
It is a descriptive statistic that shows the direction and strength of asymmetry in data. Positive values suggest right skew. Negative values suggest left skew. Values near zero suggest balance.
Which Pearson formula should I use?
Use the first coefficient when a clear mode exists. Use the second coefficient when the mode is missing, unstable, or not useful. Many reports show both values.
Can I use grouped data?
Yes. Enter lower limit, upper limit, and frequency on each line. The calculator estimates mean and deviation with midpoints. It estimates median and mode with grouped formulas.
What does a positive result mean?
A positive result means the distribution leans right. The mean is pulled toward higher values. This often happens when a few large observations stretch the upper tail.
What does a negative result mean?
A negative result means the distribution leans left. The mean is pulled toward lower values. This can happen when a few small observations stretch the lower tail.
Why is standard deviation required?
Standard deviation scales the difference between centers. This makes the coefficient unit-free. A unit-free value is easier to compare across different data sets.
What if my data has no mode?
You can use the empirical mode option. It estimates mode as three times the median minus two times the mean. You can also rely on Pearson’s second coefficient.
Can I download the result?
Yes. After calculation, use the CSV or PDF buttons above the form. The exported file includes the main statistics, coefficients, and notes.