Input a data set to instantly calculate its mean square (MS) value.
The Mean Square (MS) is the average of the squared values in a data set. It is widely used in statistics to quantify the dispersion or fluctuation within the data. Given a data set \( x_1, x_2, \dots, x_n \), the mean square (MS) is calculated using the formula: \( MS = \frac{1}{n} \sum_{i=1}^{n} x_i^2 \) Where:
Solution:
1. Square each value:
\( 1^2 = 1 \)
\( 2^2 = 4 \)
\( 3^2 = 9 \)
\( 4^2 = 16 \)
\( 5^2 = 25 \)
2. Calculate the average of the squares:
\( MS = \frac{1 + 4 + 9 + 16 + 25}{5} = \frac{55}{5} = 11 \)
Result: The mean square of this data set is 11.