XLSTAT: Skewness and Kurtosis in Excel

 

Dataset for Example

The attached data show the time (in minutes) pupils from three schools took to complete online maths and logical reasoning assessments. Rows represent pupils; columns show times and school.

We will analyze two distribution characteristics:

1. Skewness — measures asymmetry

2. Kurtosis — describes tail behavior

Using XLSTAT Descriptive Statistics, we’ll compute and interpret skewness and kurtosis for each school’s time data.

 

Setting Up

• Open XLSTAT.

• Click on the Describing data menu and select the Descriptive statistics feature.

In the General tab:

• Select the assessment time columns in Quantitative data.

• Select the school column in Subsamples.

• Check Variable-Category labels to include variable and category names.

• Choose Sheet to output results on a new sheet.

• Enable Sample labels to treat the first row as headers.

 

In the Options tab,:

• Activate the following options

. 

In the Outputs tab:

• Click on the All button to select all the statistics for quantitative data.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

Results appear on a new sheet named Desc, showing full descriptive statistics per school (columns C-H). XLSTAT provides several skewness and kurtosis coefficients; here, we use Fisher’s unbiased coefficients assuming normality. Formulas are in the XLSTAT Help menu.

Interpreting Skewness:
Skewness measures distribution asymmetry. Positive skew means a longer right tail; negative skew means a longer left tail. Zero skew indicates symmetry.

We will focus on interpreting skewness for the maths assessment.

The three samples show distinct skewness:

• Sample A: Strong positive skew (1.42) — long right tail

• Sample B: Strong negative skew (–1.63) — long left tail

• Sample C: Near-zero skew — symmetric, with mean (49.6) ≈ median (49.8)

Histograms confirm this:
Top (A) is right-skewed, middle (B) is left-skewed, and bottom (C) is symmetric.

Interpreting kurtosis:
Kurtosis reflects the weight of a distribution’s tails (outliers), using the normal distribution as a reference:

• Positive kurtosis: Fatter tails, more outliers (Leptokurtic)

• Negative kurtosis: Thinner tails, fewer outliers (Platykurtic)

• Zero kurtosis: Normal outlier behavior (Mesokurtic)

We now interpret kurtosis results for the second (logical reasoning) assessment.

 

Based on the coefficients above, the shape of the three distributions differ in terms of kurtosis:

• A positive kurtosis is estimated for School A (5.40)

• A negative one is estimated for School B (-1.32)

• A zero kurtosis was detected for School C.

Histograms confirm these observations. The top histogram (sample A) shows a leptokurtic distribution, while the second one (sample B) shows a platykurtic distribution. The third one (sample C) displays a distribution with a shape similar to the shape of a normal distribution.

Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753/