Enter a set of data to calculate both the sum of squares and the square of the sum.
The sum of squares refers to the sum of each data point squared, using the following formula: \( \text{Sum of Squares} = x_1^2 + x_2^2 + \dots + x_n^2 \) where \( x_1, x_2, \dots, x_n \) are the individual values in the data set.
The square of the sum refers to first adding all the data points together, and then squaring the total sum, using the following formula: \( \text{Square of the Sum} = (x_1 + x_2 + \dots + x_n)^2 \) Both of these concepts are very useful in statistics. For example, they are commonly used steps in calculating variance.
Solution:
1. Sum of Squares:
\( 3^2 + 5^2 + 7^2 = 9 + 25 + 49 = 83 \)
Result: Sum of Squares = 83
2. Square of the Sum:
\( (3 + 5 + 7)^2 = 15^2 = 225 \)
Result: Square of the Sum = 225
Solution:
1. Sum of Squares:
\( 2.5^2 + 4^2 + 6^2 + 8^2 + 10^2 = 6.25 + 16 + 36 + 64 + 100 = 222.25 \)
Result: Sum of Squares = 222.25
2. Square of the Sum:
\( (2.5 + 4 + 6 + 8 + 10)^2 = 30.5^2 = 930.25 \)
Result: Square of the Sum = 930.25