AR · 8 cards

Averages and Weighted Thinking flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Formula · 1/8
How do you find a simple mean?
Add the values and divide by how many there are: 12, 15, 9, 20 and 14 total 70, and $70 \div 5 = 14$ . The mean always lies between the smallest and largest values.
Formula · 2/8
What relationship links average, count and total?
$average \times count = total$ . Six deliveries averaging 45 minutes take $6 \times 45 = 270$ minutes in all.
Strategy · 3/8
Four scores must average 85; three are 82, 90 and 79. What is the fourth?
Needed total: $4 \times 85 = 340$ . Known sum: 251. Fourth score: $340 - 251 = 89$ .
Formula · 4/8
How do you combine the means of two groups of different sizes?
$\frac{n _{1} x _{1} + n _{2} x _{2}}{n _{1} + n _{2}}$ , where n is each group's size and x its mean. 15 averaging 60 and 25 averaging 68 give $2600 \div 40 = 65$ . Never just average the averages.
Formula · 5/8
How do you compute a weighted average with percent weights?
Multiply each value by its weight and add; weights totaling 100 percent need no division: $0.30 \times 95 + 0.70 \times 75 = 81$ . If weights are counts or points, divide by their sum.
Common trap · 6/8
120 miles at 40 mph, then 120 miles at 60 mph. Average speed?
48 mph: total distance over total time, $240 \div (3 + 2) = 48$ . Averaging the speeds to get 50 is wrong because more time was spent at the slower speed.
Rule · 7/8
When is the plain average of two speeds the true average speed?
Only when equal time is spent at each speed. When equal distances are covered, the true average is below the plain average because the slower leg takes longer.
Formula · 8/8
How do you find the concentration of a mix of two solutions?
Pure amount = concentration times volume. Add the pure amounts and divide by total volume: 6 L at 10 percent (0.6 L) plus 4 L at 35 percent (1.4 L) is 2 L in 10 L, or 20 percent.

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