Answer:
To determine the five-number summary of the given data, which consists of 12 winning scores, you need to arrange the scores in ascending order first. Once the data is sorted, you can find the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values.
Here are the winning scores in ascending order:
253, 266, 268, 278, 281, 286, 295, 302, 308, 315, 327, 342
Now, let's calculate the five-number summary:
1. Minimum: The minimum value is the smallest data point, which is 253.
2. Lower Quartile (Q1): The lower quartile divides the lower 25% of the data. To find Q1, we'll calculate the median of the lower half of the data, which is the middle value between the first and sixth data points (since there are 12 data points).
Q1 = (268 + 278) / 2 = 273
3. Median (Q2): The median is the middle value of the sorted data. Since there are 12 data points, the median is the average of the sixth and seventh data points.
Q2 = (286 + 295) / 2 = 290.5
4. Upper Quartile (Q3): The upper quartile divides the upper 25% of the data. To find Q3, we'll calculate the median of the upper half of the data, which is the middle value between the seventh and twelfth data points.
Q3 = (315 + 327) / 2 = 321
5. Maximum: The maximum value is the largest data point, which is 342.
So, the five-number summary of the data is as follows:
- Minimum: 253
- Lower Quartile (Q1): 273
- Median (Q2): 290.5
- Upper Quartile (Q3): 321
- Maximum: 342