To determine how the median test scores of the 4th and 6th-period classes compare, we'll need to follow a series of steps, which include arranging the scores in ascending order and finding the median for each period.
Let's begin with the 4th period scores:
[tex]\[ \{90, 83, 87, 82, 89, 82\} \][/tex]
1. First, arrange the scores in ascending order:
[tex]\[ \{82, 82, 83, 87, 89, 90\} \][/tex]
2. Since there are six scores, the median is the average of the 3rd and 4th scores:
[tex]\[ \text{Median} = \frac{83 + 87}{2} = \frac{170}{2} = 85.0 \][/tex]
Next, let’s consider the 6th period scores:
[tex]\[ \{86, 81, 88, 90, 88, 85\} \][/tex]
1. Again, arrange the scores in ascending order:
[tex]\[ \{81, 85, 86, 88, 88, 90\} \][/tex]
2. Similarly, the median is the average of the 3rd and 4th scores:
[tex]\[ \text{Median} = \frac{86 + 88}{2} = \frac{174}{2} = 87.0 \][/tex]
Now, we have the medians for the 4th and 6th periods:
- Median of the 4th period: 85.0
- Median of the 6th period: 87.0
We can compare these medians:
- The median test score of the 6th period (87.0) is greater than the median test score of the 4th period (85.0).
- The difference between the medians is [tex]\(87.0 - 85.0 = 2.0\)[/tex].
Based on this comparison:
D. The median test score of the 6th period is greater than the median test score of the 4th period by 2 points.
