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Answer :
Let's find the mean, median, mode, and midrange for the given test scores step-by-step.
First, let's list the test scores given in the problem:
[tex]\[ 88, 82, 97, 76, 79, 92, 65, 84, 79, 90, 75, 82, 78, 77, 93, 88, 95, 73, 69, 89, 93, 78, 60, 95, 88, 72, 80, 94, 88, 74 \][/tex]
1. Mean:
The mean (average) is calculated by adding all the numbers together and dividing by the count of numbers.
[tex]\[
\text{Sum of scores} = 88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 + 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74 = 2472
\][/tex]
Total number of scores = 30
[tex]\[
\text{Mean} = \frac{2472}{30} = 82.4
\][/tex]
2. Median:
The median is the middle number in a sorted, ascending or descending, list of numbers.
First, we sort the scores:
[tex]\[
60, 65, 69, 72, 73, 74, 75, 76, 77, 78, 78, 79, 79, 80, 82, 82, 84, 88, 88, 88, 88, 89, 90, 92, 93, 93, 94, 95, 95, 97
\][/tex]
Since there are 30 scores, which is an even number, the median is the average of the 15th and 16th numbers in the sorted list.
15th number = 82 and 16th number = 82
[tex]\[
\text{Median} = \frac{82 + 82}{2} = 82
\][/tex]
3. Mode:
The mode is the number that appears most frequently in the list of numbers.
Looking at the sorted scores, we can see that 88 appears four times, which is more frequent than any other number.
[tex]\[
\text{Mode} = 88
\][/tex]
4. Midrange:
The midrange is the average of the maximum and minimum numbers in the list.
Maximum score = 97, Minimum score = 60
[tex]\[
\text{Midrange} = \frac{97 + 60}{2} = 78.5
\][/tex]
Finally, based on these calculations:
- Mean: 82.4
- Median: 82
- Mode: 88
- Midrange: 78.5
The correct answer is option d: Mean is 82.4, median is 82, mode is 88, midrange is 78.5.
First, let's list the test scores given in the problem:
[tex]\[ 88, 82, 97, 76, 79, 92, 65, 84, 79, 90, 75, 82, 78, 77, 93, 88, 95, 73, 69, 89, 93, 78, 60, 95, 88, 72, 80, 94, 88, 74 \][/tex]
1. Mean:
The mean (average) is calculated by adding all the numbers together and dividing by the count of numbers.
[tex]\[
\text{Sum of scores} = 88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 + 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74 = 2472
\][/tex]
Total number of scores = 30
[tex]\[
\text{Mean} = \frac{2472}{30} = 82.4
\][/tex]
2. Median:
The median is the middle number in a sorted, ascending or descending, list of numbers.
First, we sort the scores:
[tex]\[
60, 65, 69, 72, 73, 74, 75, 76, 77, 78, 78, 79, 79, 80, 82, 82, 84, 88, 88, 88, 88, 89, 90, 92, 93, 93, 94, 95, 95, 97
\][/tex]
Since there are 30 scores, which is an even number, the median is the average of the 15th and 16th numbers in the sorted list.
15th number = 82 and 16th number = 82
[tex]\[
\text{Median} = \frac{82 + 82}{2} = 82
\][/tex]
3. Mode:
The mode is the number that appears most frequently in the list of numbers.
Looking at the sorted scores, we can see that 88 appears four times, which is more frequent than any other number.
[tex]\[
\text{Mode} = 88
\][/tex]
4. Midrange:
The midrange is the average of the maximum and minimum numbers in the list.
Maximum score = 97, Minimum score = 60
[tex]\[
\text{Midrange} = \frac{97 + 60}{2} = 78.5
\][/tex]
Finally, based on these calculations:
- Mean: 82.4
- Median: 82
- Mode: 88
- Midrange: 78.5
The correct answer is option d: Mean is 82.4, median is 82, mode is 88, midrange is 78.5.
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