Enter a set of numbers to calculate the 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:
The formula is: \( \text{Cubic Mean} = \sqrt[3]{\frac{1}{n} \sum_{i=1}^{n} x_i^3} \) Where:
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.
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.