Question

final score on balance beam in women’s gymnastics
11, 15, 13, 18, 9, 14, 16, 12, 7
ascending order:
lower extreme: ____
lower quartile: ____
median: ____
upper quartile: ____
upper extreme: ____

Explanation:

Step1: Sort the data

First, we sort the given scores in ascending order. The original scores are 11, 15, 13, 18, 9, 14, 16, 12. After sorting, we get: 9, 11, 12, 13, 14, 15, 16, 18.

Step2: Find the Lower Extreme

The lower extreme is the minimum value in the dataset. From the sorted data, the minimum value is 9.

Step3: Find the Median

The dataset has 8 values (even number of observations). The median is the average of the two middle numbers. The two middle numbers are the 4th and 5th values. The 4th value is 13 and the 5th value is 14. So the median is $\frac{13 + 14}{2} = \frac{27}{2} = 13.5$.

Step4: Find the Lower Quartile (Q1)

The lower quartile is the median of the lower half of the data. The lower half of the data (for 8 values, the first 4 values) is 9, 11, 12, 13. The median of these 4 values (even number) is the average of the 2nd and 3rd values. The 2nd value is 11 and the 3rd value is 12. So Q1 is $\frac{11 + 12}{2} = \frac{23}{2} = 11.5$.

Step5: Find the Upper Quartile (Q3)

The upper quartile is the median of the upper half of the data. The upper half of the data (the last 4 values) is 14, 15, 16, 18. The median of these 4 values (even number) is the average of the 2nd and 3rd values. The 2nd value is 15 and the 3rd value is 16. So Q3 is $\frac{15 + 16}{2} = \frac{31}{2} = 15.5$.

Step6: Find the Upper Extreme

The upper extreme is the maximum value in the dataset. From the sorted data, the maximum value is 18.

Answer:

• Lower Extreme: 9
• Lower Quartile: 11.5
• Median: 13.5
• Upper Quartile: 15.5
• Upper Extreme: 18