To determine the most favorable measure of central tendency for your test scores (89, 81, 85, 82, 89, and 89), we will calculate the mean, median, and mode.
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Mean (Average): \[ \text{Mean} = \frac{\text{Sum of scores}}{\text{Number of scores}} = \frac{89 + 81 + 85 + 82 + 89 + 89}{6} \] \[ = \frac{515}{6} \approx 85.83 \] Rounded to the nearest whole number, the mean is 86.
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Median: First, we need to arrange the scores in ascending order: 81, 82, 85, 89, 89, 89. With six values (an even number), the median is the average of the two middle numbers (3rd and 4th): \[ \text{Median} = \frac{85 + 89}{2} = \frac{174}{2} = 87 \]
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Mode: The mode is the number that appears most frequently: The score 89 appears three times, which is more than any other score. Thus, the mode is 89.
Now, let's summarize the results:
- Mean: 86
- Median: 87
- Mode: 89
The most favorable measure to choose would be the mode since it gives the highest score, which could be advantageous for your grade determination.
Therefore, your grade to the nearest whole number is 89, and the most favorable measure of central tendency to choose is mode.
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