To calculate Derrick's mean and median test scores, let's start by organizing the data:
Scores: 25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Mean Calculation:
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Sum of all scores: \[ 25 + 40 + 68 + 70 + 78 + 85 + 85 + 95 + 98 + 100 = 814 \]
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Number of scores: There are 10 scores.
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Mean: \[ \text{Mean} = \frac{\text{Sum of scores}}{\text{Number of scores}} = \frac{814}{10} = 81.4 \]
Median Calculation:
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Ordering the scores (already ordered): 25, 40, 68, 70, 78, 85, 85, 95, 98, 100
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Finding the median: Since there are 10 numbers (an even number), the median is the average of the two middle scores (5th and 6th scores): The 5th score is 78, and the 6th score is 85. \[ \text{Median} = \frac{78 + 85}{2} = \frac{163}{2} = 81.5 \]
Summary:
- Mean Score: 81.4
- Median Score: 81.5
Which Gives a Better Picture of His Scores?
Both the mean and median give a good picture of Derrick's scores, but they can tell different stories:
- The mean can be influenced by extremely low or high values. In this case, the low score of 25 might pull the mean down slightly.
- The median provides a better measure of central tendency when the data has outliers or is skewed.
In conclusion, since Derrick has a low outlier (25), the median (81.5) might give a better picture of his performance overall as it suggests that half of his scores were above this point.
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