To find the range and mean of each player's batting averages, we'll first organize and calculate for each player.
Player 1 Batting Averages:
- Averages: 0.202, 0.364, 0.333, 0.276, 0.281, 0.277
Calculating Range:
- Maximum: The highest value is 0.364.
- Minimum: The lowest value is 0.202.
- Range = Maximum - Minimum = 0.364 - 0.202 = 0.162
Calculating Mean: \[ \text{Mean} = \frac{\text{Sum of averages}}{\text{Number of seasons}} = \frac{0.202 + 0.364 + 0.333 + 0.276 + 0.281 + 0.277}{6} \] \[ = \frac{1.733}{6} \approx 0.2888 \]
Player 2 Batting Averages:
- Averages: 0.324, 0.338, 0.296, 0.238, 0.327, 0.196
Calculating Range:
- Maximum: The highest value is 0.338.
- Minimum: The lowest value is 0.196.
- Range = Maximum - Minimum = 0.338 - 0.196 = 0.142
Calculating Mean: \[ \text{Mean} = \frac{\text{Sum of averages}}{\text{Number of seasons}} = \frac{0.324 + 0.338 + 0.296 + 0.238 + 0.327 + 0.196}{6} \] \[ = \frac{1.719}{6} \approx 0.2865 \]
Summary of Results:
-
Player 1:
- Range: 0.162
- Mean: 0.2888
-
Player 2:
- Range: 0.142
- Mean: 0.2865
Comparison:
- The mean of Player 1 (0.2888) is slightly higher than the mean of Player 2 (0.2865), indicating that Player 1 has a marginally better overall batting average across the six seasons.
- The range for Player 1 (0.162) is greater than that of Player 2 (0.142), which suggests that Player 1 had more variability in their performance levels than Player 2. Player 1 had a performance peak at 0.364 while Player 2's peak was lower (0.338).
In summary, while Player 1 has a slightly better mean and more variability in their performance, both players have their strengths and weaknesses reflected in their batting averages.
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