To calculate the five-number summary (minimum, Q1, median, Q3, and maximum) for the data set of test scores, we will first sort the scores in ascending order:
Sorted scores: 74, 84, 89, 90, 93, 95, 97, 99
Next, we will calculate each of the five-number summary components:
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Minimum: The smallest value in the dataset.
- Minimum = 74
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Maximum: The largest value in the dataset.
- Maximum = 99
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Median: The middle value of the dataset. Since there are 9 scores (an odd number), the median is the 5th value in the sorted list.
- Median = 93
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Q1 (First Quartile): This is the median of the lower half of the dataset (the scores below the median). The lower half consists of: 74, 84, 89, 90 (4 values).
- Q1 is the average of the 2nd and 3rd values: (84 + 89) / 2 = 86.5
- Q1 = 86.5
-
Q3 (Third Quartile): This is the median of the upper half of the dataset (the scores above the median). The upper half consists of: 95, 97, 99 (4 values).
- Q3 is the average of the 2nd and 3rd values: (97 + 95) / 2 = 96
- Q3 = 96
Now we can summarize the values:
- The minimum is 74.
- The value for Q1 is 86.5.
- The median of the dataset is 93.
- The value for Q3 is 96.
- The maximum of the dataset is 99.
So the five-number summary is:
- Minimum = 74
- Q1 = 86.5
- Median = 93
- Q3 = 96
- Maximum = 99