Homework Sourse1 Below shown two NBA players scoring points per game a Whic
1. Below shown two NBA players’ scoring points per game:
a) Which player is better? Show all the calculations
b) Which player’s performance is more consistent? Use all the sample points and show all thecalculations
| GAME | PLAYER A | PLAYER B |
| 1 | 21 | 34 |
| 2 | 52 | 29 |
| 3 | 15 | 29 |
| 4 | 10 | 22 |
| 5 | 29 | 36 |
| 6 | 29 | 27 |
| 7 | 29 | 25 |
| 8 | 27 | 12 |
Solution
a)
For player A:
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 212
As n = 8
Thus,
X = 26.5
For player B:
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 214
As n = 8
Thus,
X = 26.75
Thus, as player B has a greater mean, PLAYER B IS BETTER. [ANSWER]
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b)
To see who is more consistent, we get the standard deviations.
For player A:
Setting up tables,
x x - X (x - X)^2
21 -5.5 30.25
52 25.5 650.25
15 -11.5 132.25
10 -16.5 272.25
29 2.5 6.25
29 2.5 6.25
29 2.5 6.25
27 0.5 0.25
Thus, Sum(x - X)^2 = 1104
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 8
s^2 = 157.7142857
Thus,
s = 12.55843484
For Player B:
Setting up tables,
x x - X (x - X)^2
34 7.25 52.5625
29 2.25 5.0625
29 2.25 5.0625
22 -4.75 22.5625
36 9.25 85.5625
27 0.25 0.0625
25 -1.75 3.0625
12 -14.75 217.5625
Thus, Sum(x - X)^2 = 391.5
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 8
s^2 = 55.92857143
Thus,
s = 7.478540729
As player B has lesser standard deviation, then PLAYER B IS MORE CONSISTENT. [ANSWER]
