# Skewness vs. Kurtosis: What's the Difference?

Edited by Huma Saeed || By Sawaira Riaz || Published on December 18, 2023
"Skewness measures asymmetry in data distribution; kurtosis assesses the 'tailedness' or extremity of data distribution."

## Key Differences

Skewness quantifies how much a distribution deviates from symmetry, indicating whether data tails are stretched on one side. Kurtosis measures the 'peakedness' or 'flatness' of a distribution, indicating the presence of outliers.
Sawaira Riaz
Dec 18, 2023
A skewness value of zero indicates a perfectly symmetrical distribution, whereas nonzero values suggest a skew to the left or right. Kurtosis values, in comparison, show whether data tails are heavier or lighter than a normal distribution.
Sawaira Riaz
Dec 18, 2023
Positive skewness means the tail is on the right side, showing a majority of values are low; negative skewness is the opposite. High kurtosis indicates a distribution with heavy tails and a sharp peak, suggesting outliers are more likely.
Huma Saeed
Dec 18, 2023
Skewness is crucial in risk management for understanding distribution asymmetry. Kurtosis is important for assessing the risk of extreme values, which can be critical in fields like finance.
Aimie Carlson
Dec 18, 2023
In data analysis, skewness is used to adjust models for asymmetric data. Kurtosis, on the other hand, helps in identifying potential problems with outliers in datasets.
Sawaira Riaz
Dec 18, 2023

## Comparison Chart

### Definition

Measures asymmetry in data distribution
Measures 'tailedness' of data distribution
Sawaira Riaz
Dec 18, 2023

### Value Interpretation

Zero for symmetry, positive/negative skew
High values indicate heavy tails
Sawaira Riaz
Dec 18, 2023

### Importance in Analysis

Indicates direction of data tail
Indicates extremity of outliers
Sawaira Riaz
Dec 18, 2023

### Application

Used in risk management and data modeling
Helps identify outlier impact in data
Harlon Moss
Dec 18, 2023

### Visual Representation

Skewed left/right graphs
Peaked/flat distribution graphs
Sawaira Riaz
Dec 18, 2023

## Skewness and Kurtosis Definitions

#### Skewness

A statistic that reflects deviation from the normal distribution.
High skewness indicated a non-normal distribution.
Janet White
Dec 06, 2023

#### Kurtosis

Measure of tail heaviness in a distribution.
High kurtosis indicated more outliers in the dataset.
Huma Saeed
Dec 06, 2023

#### Skewness

Indicator of how lopsided a distribution is.
The skewness showed a rightward tail in sales data.
Janet White
Dec 06, 2023

#### Kurtosis

Indicator of peakedness or flatness of data.
The low kurtosis suggested a flatter distribution.
Harlon Moss
Dec 06, 2023

#### Skewness

Measure of distribution asymmetry.
The skewness of the income data was positive.
Sawaira Riaz
Dec 06, 2023

#### Kurtosis

Describes the tendency of data to produce outliers.
Kurtosis was crucial in understanding the stock market's volatility.
Janet White
Dec 06, 2023

#### Skewness

A descriptor of data tail length and direction.
Negative skewness meant a longer left tail in the dataset.
Harlon Moss
Dec 06, 2023

#### Kurtosis

A statistic reflecting the extremity of data points.
The kurtosis was analyzed to assess financial risk.
Harlon Moss
Dec 06, 2023

#### Skewness

Quantitative representation of distribution shape.
The skewness value was used to adjust the statistical model.
Janet White
Dec 06, 2023

#### Kurtosis

Quantifies the shape of distribution tails.
The kurtosis value indicated heavier tails than a normal distribution.
Aimie Carlson
Dec 06, 2023

#### Skewness

To turn or place at an angle
Skew the cutting edge of a plane.
Sawaira Riaz
Dec 06, 2023

#### Kurtosis

A quantity indicating how sharply a probability distribution function increases and decreases around the distribution's mean.
Sawaira Riaz
Dec 06, 2023

#### Skewness

To give a bias to; distort
The use of a limited sample skewed the findings of the study.
Sawaira Riaz
Dec 06, 2023

#### Kurtosis

(statistics) A measure of "heaviness of the tails" of a probability distribution, defined as the fourth cumulant divided by the square of the variance of the probability distribution.
Sawaira Riaz
Dec 06, 2023

#### Kurtosis

(statistics) Excess kurtosis: the difference between a given distribution's kurtosis and the kurtosis of a normal distribution.
Sawaira Riaz
Dec 06, 2023

## FAQs

#### Can skewness be negative?

Yes, indicating a longer tail on the left side.
Sawaira Riaz
Dec 18, 2023

#### Is skewness relevant in normal distributions?

Yes, it helps determine if the distribution deviates from normality.
Sawaira Riaz
Dec 18, 2023

#### What does a skewness of zero mean?

It indicates a perfectly symmetrical distribution.
Sawaira Riaz
Dec 18, 2023

#### Does high kurtosis mean a sharp peak?

Yes, along with heavy tails.
Sawaira Riaz
Dec 18, 2023

#### Does skewness impact hypothesis testing?

Yes, especially in tests assuming normality.
Aimie Carlson
Dec 18, 2023

#### Is high kurtosis good or bad?

It depends on the context; it can indicate higher risk of outliers.
Huma Saeed
Dec 18, 2023

#### How is skewness calculated?

Using a formula that involves the third moment about the mean.
Janet White
Dec 18, 2023

#### What does right-skewed data imply?

Most values are on the lower side, with few higher values.
Sawaira Riaz
Dec 18, 2023

#### Can skewness be used to predict future trends?

Indirectly, as it shows distribution tendencies.
Sawaira Riaz
Dec 18, 2023

#### Can skewness affect statistical analysis?

Absolutely, especially in model accuracy and assumption testing.
Sawaira Riaz
Dec 18, 2023

#### Does kurtosis have units?

No, it's a dimensionless measure.
Sawaira Riaz
Dec 18, 2023

#### Can kurtosis be negative?

Yes, indicating lighter tails than a normal distribution.
Sawaira Riaz
Dec 18, 2023

#### What's the relation between kurtosis and variance?

Kurtosis is related but not directly proportional to variance.
Harlon Moss
Dec 18, 2023

#### Is kurtosis a measure of central tendency?

No, it measures tail extremity, not central tendency.
Janet White
Dec 18, 2023

#### What does kurtosis reveal about data?

It reveals the presence and extremity of outliers.
Harlon Moss
Dec 18, 2023

#### How does kurtosis affect financial models?

It impacts the assessment of investment risk.
Sawaira Riaz
Dec 18, 2023

#### Should skewness be corrected in data analysis?

It often should be, to meet model assumptions.
Janet White
Dec 18, 2023

Harlon Moss
Dec 18, 2023

#### Is zero skewness common in real-world data?

No, perfectly symmetrical data is rare in practice.
Janet White
Dec 18, 2023

#### Are kurtosis values standardized?

There are standard measures, but interpretation varies by field.
Aimie Carlson
Dec 18, 2023