Skewness And Kurtosis Calculator

Skewness And Kurtosis Formulas:

\[ Skewness = \frac{\sum (x_i - \mu)^3}{n \sigma^3} \] \[ Kurtosis = \frac{\sum (x_i - \mu)^4}{n \sigma^4} \]

Skewness:

Kurtosis:

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1. What Are Skewness And Kurtosis?

Skewness and Kurtosis are statistical measures that describe the shape of a probability distribution. Skewness measures the asymmetry of the distribution, while Kurtosis measures the "tailedness" or peakiness of the distribution compared to a normal distribution.

2. How Does The Calculator Work?

The calculator uses the population formulas for Skewness and Kurtosis:

\[ Skewness = \frac{\sum (x_i - \mu)^3}{n \sigma^3} \] \[ Kurtosis = \frac{\sum (x_i - \mu)^4}{n \sigma^4} \]

Where:

\( x_i \) — Individual data points
\( \mu \) — Mean of the data
\( n \) — Number of data points
\( \sigma \) — Standard deviation of the data

Explanation: Skewness measures the degree of asymmetry in the distribution, while Kurtosis measures whether the data are heavy-tailed or light-tailed relative to a normal distribution.

3. Importance Of Skewness And Kurtosis

Details: Skewness helps identify if data is symmetric (skewness ≈ 0), right-skewed (positive), or left-skewed (negative). Kurtosis indicates if data has more (leptokurtic, kurtosis > 3) or fewer (platykurtic, kurtosis < 3) extreme values than a normal distribution.

4. Using The Calculator

Tips: Enter numerical data points separated by commas. The calculator will compute the population skewness and kurtosis. Ensure you have at least 3 data points for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What does positive skewness indicate?
A: Positive skewness indicates the distribution has a longer tail on the right side, with most values concentrated on the left.

Q2: What does negative skewness indicate?
A: Negative skewness indicates the distribution has a longer tail on the left side, with most values concentrated on the right.

Q3: What is mesokurtic distribution?
A: Mesokurtic distribution has kurtosis ≈ 3, similar to a normal distribution in terms of tailedness.

Q4: What is leptokurtic distribution?
A: Leptokurtic distribution has kurtosis > 3, indicating heavier tails and more extreme values than a normal distribution.

Q5: What is platykurtic distribution?
A: Platykurtic distribution has kurtosis < 3, indicating lighter tails and fewer extreme values than a normal distribution.