Cubic Mean Calculator

Enter a set of numbers to calculate the cubic mean.

Calculate the Cubic Mean

Result

What Is Cubic Mean?

The cubic mean is a method for calculating the average of a dataset, particularly useful in scenarios involving growth rates or weighted data. By averaging the cubes of the dataset values and then taking the cube root, the cubic mean offers an accurate representation of datasets with large numerical variations.

For a dataset \( x_1, x_2, \dots, x_n \), the cubic mean is calculated as follows:

Cube Each Data Point: Raise each data point to the power of three and sum them.
Find the Average of Cubes: Divide the sum of the cubes by the total number of data points (\( n \)).
Take the Cube Root: Compute the cube root of the result to obtain the cubic mean.

The formula is: \( \text{Cubic Mean} = \sqrt[3]{\frac{1}{n} \sum_{i=1}^{n} x_i^3} \) Where:

\( x_i \) is each data point in the dataset.
\( n \) is the total number of data points.

Examples

Example 1: Compute the cubic mean for the data set [2, 3, 4]

Solution:

1. Cube each data point and sum them:

\( 2^3 + 3^3 + 4^3 = 8 + 27 + 64 = 99 \)

2. Divide by the number of data points (\( n = 3 \)):

\( \frac{99}{3} = 33 \)

3. Take the cube root of the result:

\( \sqrt[3]{33} \approx 3.207 \)

Result: The cubic mean is approximately 3.207.

Example 2: Compute the cubic mean for the data set [5, 7, 9]

Solution:

1. Cube each data point and sum them:

\( 5^3 + 7^3 + 9^3 = 125 + 343 + 729 = 1197 \)

2. Divide by the number of data points (\( n = 3 \)):

\( \frac{1197}{3} = 399 \)

3. Take the cube root of the result:

\( \sqrt[3]{399} \approx 7.37 \)

Result: The cubic mean is approximately 7.37.