SUMSQ

Returns the sum of the squares of the arguments.

Syntax:

SUMSQ(number1, number2, .... number30)

number1 to number30 are up to 30 numbers or ranges of numbers which are squared and then summed.

Example:

SUMSQ(2, 3, 4)

returns 29, which is 2*2 + 3*3 + 4*4.

SUMSQ(A1:A2)

where A1 contains 1 and A2 contains 2 returns 5, which is 1*1 + 2*2.

Application:

Analyzing a Company's Monthly Website Traffic Variance

Scenario: A marketing analyst at a company wants to understand the month-to-month variability in their website's organic search traffic. A simple sum or average doesn't capture the magnitude of the changes. The sum of squares is a key component in calculating statistical measures like variance and standard deviation, which are perfect for this kind of analysis.

Function: The SUMSQ function calculates the sum of the squares of a set of numbers. The formula is:

$SUMSQ (x_{1}, x_{2}, \dots, x_{n}) = x_{1}^{2} + x_{2}^{2} + \dots + x_{n}^{2}$

Data Table: The analyst has the following data for the first six months of the year, showing the difference from the previous month's organic search sessions.

	Month	Month-over-Month Change in Sessions
	A	B
1	January	150
2	February	-75
3	March	220
4	April	50
5	May	-180
6	June	100

Applying the SUMSQ function:

The analyst wants to find the sum of the squares of these changes to get a measure of the total squared deviation. This value is often used as a precursor to calculating the variance.

The formula would be: SUMSQ(150, -75, 220, 50, -180, 100)

Calculation:

The function performs the following steps:

Square each number in the list:
- 1502=22,500
- (−75)2=5,625
- 2202=48,400
- 502=2,500
- (−180)2=32,400
- 1002=10,000
Sum the results:
- 22,500+5,625+48,400+2,500+32,400+10,000=121,425

Result:

The result of the SUMSQ function is 121,425.

Result from SUMSQ(150, -75, 220, 50, -180, 100):

121,425

Interpretation:

This value, while not a final metric on its own, is a critical component for the analyst. The larger the sum of squares, the greater the overall variability of the website traffic. The analyst could use this value to calculate the sample variance by dividing it by the number of observations minus one (121,425/5=24,285), giving them a robust statistical measure of the traffic's volatility. This helps them determine if the organic traffic is stable or if it experiences significant and unpredictable swings.