Answer :
Sure! Let's go through the calculations step-by-step to determine the mean, median, mode, and midrange for the given set of class test scores.
### Test Scores:
These are the scores we have:
88, 82, 97, 76, 79, 92, 65, 84, 79, 90, 75, 82, 78, 77, 93, 88, 95, 73, 69, 89, 93, 78, 60, 95, 88, 72, 80, 94, 88, 74.
### Mean:
To find the mean, add up all the scores and then divide by the number of scores.
1. Add all the scores: [tex]\( 88 + 82 + 97 + \ldots + 88 + 74 = 2473 \)[/tex]
2. Count the number of scores (n): There are 30 scores.
3. Divide the sum by the number of scores:
[tex]\[
\text{Mean} = \frac{2473}{30} \approx 82.4
\][/tex]
### Median:
The median is the middle value when the scores are arranged in ascending order.
1. Sort the scores: 60, 65, 69, 72, 73, 74, 75, 76, 77, 78, 78, 79, 79, 80, 82, 82, 84, 88, 88, 88, 88, 89, 90, 92, 93, 93, 94, 95, 95, 97.
2. Since there are 30 scores, the median will be the average of the 15th and 16th scores.
3. The 15th and 16th scores are both 82.
[tex]\[
\text{Median} = \frac{82 + 82}{2} = 82
\][/tex]
### Mode:
The mode is the score that appears most frequently.
- From the sorted list, the score 88 appears the most often.
### Midrange:
The midrange is calculated by averaging the highest and lowest scores.
1. The lowest score is 60, and the highest score is 97.
2. Calculate the midrange:
[tex]\[
\text{Midrange} = \frac{60 + 97}{2} = 78.5
\][/tex]
Based on this detailed step-by-step calculation, the correct answer is that the mean is 82.4, median is 82, mode is 88, and midrange is 78.5. Therefore, option D: Mean is 82.4, median is 82, mode is 88, midrange is 78.5 is the best answer.
### Test Scores:
These are the scores we have:
88, 82, 97, 76, 79, 92, 65, 84, 79, 90, 75, 82, 78, 77, 93, 88, 95, 73, 69, 89, 93, 78, 60, 95, 88, 72, 80, 94, 88, 74.
### Mean:
To find the mean, add up all the scores and then divide by the number of scores.
1. Add all the scores: [tex]\( 88 + 82 + 97 + \ldots + 88 + 74 = 2473 \)[/tex]
2. Count the number of scores (n): There are 30 scores.
3. Divide the sum by the number of scores:
[tex]\[
\text{Mean} = \frac{2473}{30} \approx 82.4
\][/tex]
### Median:
The median is the middle value when the scores are arranged in ascending order.
1. Sort the scores: 60, 65, 69, 72, 73, 74, 75, 76, 77, 78, 78, 79, 79, 80, 82, 82, 84, 88, 88, 88, 88, 89, 90, 92, 93, 93, 94, 95, 95, 97.
2. Since there are 30 scores, the median will be the average of the 15th and 16th scores.
3. The 15th and 16th scores are both 82.
[tex]\[
\text{Median} = \frac{82 + 82}{2} = 82
\][/tex]
### Mode:
The mode is the score that appears most frequently.
- From the sorted list, the score 88 appears the most often.
### Midrange:
The midrange is calculated by averaging the highest and lowest scores.
1. The lowest score is 60, and the highest score is 97.
2. Calculate the midrange:
[tex]\[
\text{Midrange} = \frac{60 + 97}{2} = 78.5
\][/tex]
Based on this detailed step-by-step calculation, the correct answer is that the mean is 82.4, median is 82, mode is 88, and midrange is 78.5. Therefore, option D: Mean is 82.4, median is 82, mode is 88, midrange is 78.5 is the best answer.
