Find a weighted mean

Average values when some count for more than others, such as graded work with different weights.

In a weighted mean each value is multiplied by its weight, the results are added, and the total is divided by the sum of the weights.

The example: a test score of 80 counts 3 times and a score of 90 counts 2 times. The weighted mean is (80 × 3 + 90 × 2) ÷ 5 = 84.

The Classic financial-style RPN models and the Advanced RPN model have a dedicated weighted-mean key. Others do the same job with a frequency list.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

Type the scores in L1 and the weights in L2.
stat180enter90enter▶3enter2enter
Open 1-Var Stats (STAT, CALC, option 1).
stat▶1
Put L2 in the FreqList box, then calculate. The mean x̄ is the weighted mean.
▼2ndL22▼enter

You should seex̄=84 Σx=420 n=5

Classic Graphing 84 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

Turn on the frequency column: SHIFT, MENU for Setup, Statistics (option 6), On.
SHIFTSETUPMENU61
Open Statistics, choose 1-Variable and type the scores in x.
MENU6180=90=
Move right, go back to the top and type the weights in Freq.
▶▲▲3=2=AC
Press OPTN and choose 1-Variable Calc. x̄ is the weighted mean.
OPTN3

You should seex̄=84 Σx=420

Natural Scientific 991 key reference

RPN Financial 12

Start on the main screen: There is no menu to leave: the display always shows the X register. Press f then R/S (P/R) to leave program mode, and clear a pending prefix by pressing ON.

Clear the statistics registers with f then CLx.
fREGCLx
For each item key in the value, press ENTER, key in its weight and press Σ+.
80ENTER3Σ+90ENTER2Σ+
Press g then 6, the weighted-mean key x̄w.
gx̄w6

You should see84.00

RPN Financial 12 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

For each item key in the weight, press ENTER, key in the value and press the Σ+ key.
3ENTER80Σ+2ENTER90Σ+
Open the STAT menu (shift then ÷) and press the fourth key, x̄w.
⇧STAT÷LOG

You should seex: 84.0000

Notice the order: the Advanced RPN 42 takes the weight first, while the Financial RPN 12 takes the value first.

RPN Advanced 42 key reference

Tips

Weights do not have to add up to 100. Only their proportions matter.