Question

Consider the following scenario to understand the relationship between marginal and average values. Suppose Kyoko is a professional basketball player, and her game log for free throws can be summarized in the following table. Fill in the columns with Kyoko's free-throw percentage for each game and her overall free-throw average after each game. Game Game Free-Throw Average Free-Throw Game Result Total Percentage Percentage 1 8/10 8/10 80 80 2 4/10 12/20 3 2/8 14/28 4 2/4 16/32 5 6/8 22/40 On the following graph, use the orange points (square symbol) to plot Kyoko's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her overall average free-throw percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. ? 100 90 Game Free-Throw Percentage 80 70 60 Average Free-Throw Percentage FREE-THROW PERCENTAGE 50 40 30 20 10 0 GAME You can think of the result in any one game as being Kyoko's marginal free-throw percentage. Based on your previous answer, you can deduce that when Kyoko's marginal free-throw percentage is above the average, the average must be

Answer 1

Game Free Throw percentage = Game result * 100

Average Free Throw percentage = Total * 100

Game	Game result	Total	Game Free Throw percentage	Average Free Throw percentage
1	8/10	8/10	80	80
2	4/10	12/20	40	60
3	2/8	14/28	25	50
4	2/4	16/32	50	50
5	6/8	22/40	75	55

90 80 70 60 Game Free Throw percentage 50 40 -Average Free Throw percentage 30 20 10 0 1 2 3 4 5

Blank 1: rising

Blank 2: falling

Blank 3: rising

Blank 4: at its minimum