Weighted Average

The Weighted Average calculator computes the weighted average from two groups based on their averages (means) and group sizes.

INSTRUCTIONS: Enter the following:

• (S1) This is the size of group 1.
• (A1) This is average (mean) of group 1.
• (S2) This is the size of group 2.
• (A2) This is the average of group 2. 

Weighted Average: The calculator returns the weighted average of the two groups. 

Related Calcs:

• To compute the mean of a group of numbers, CLICK HERE.

The Math

If you consider the following two groups:

• Group 1:  23,15,87,15,67,43,28,22,17,19   Group Size: 10  Mean: 33.6
• Group 2:  28,67,91,15,4                             Group Size:   5  Mean: 41.0

If you take the average of the two means:

                `(33.6 + 41.0)/2 = 37.3` you do not take into consideration that Group 1 had twice as many observations.

To compute the weighted average:

                `WA = (10 * 33.6 + 5 * 41)/(10 + 5) = 36.066

This takes into account the larger size of Group 1.