Select the correct answer.

Below are the average test scores of two different math class periods.

| | Test 1 | Test 2 | Test 3 | Test 4 | Test 5 | Test 6 |
|---------|--------|--------|--------|--------|--------|--------|
| 4th period | 90 | 83 | 87 | 82 | 89 | 82 |
| 6th period | 86 | 81 | 88 | 90 | 88 | 85 |

How do the median test scores of each class period compare?

A. The median test score of 4th period is equal to the median test score of 6th period.
B. The median test score of 6th period is greater than the median test score of 4th period by 1 point.
C. The median test score of 4th period is greater than the median test score of 6th period by 2 points.
D. The median test score of 6th period is greater than the median test score of 4th period by 2 points.



Answer :

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.