Answer :
To determine which statistical measure is most affected by the lowest score, we need to understand how each measure is calculated and how outliers influence them.
### Mean:
The mean (average) is calculated by summing all the scores and dividing by the number of scores.
Given scores: \( 82, 83, 80, 89, 86, 35, 86, 90, 86, 87 \)
Sum of scores: \( 82 + 83 + 80 + 89 + 86 + 35 + 86 + 90 + 86 + 87 = 804 \)
Number of scores: \( 10 \)
Mean: \( \frac{804}{10} = 80.4 \)
If the lowest score (35) were removed, the sum would be:
New sum: \( 804 - 35 = 769 \)
New mean without the lowest score: \( \frac{769}{9} \approx 85.44 \)
You can see that the mean changes significantly when the lowest score (35) is removed.
### Median:
The median is the middle value in a list when the numbers are arranged in ascending order.
Arranged scores: \( 35, 80, 82, 83, 86, 86, 86, 87, 89, 90 \)
Here, we have an even number of scores (10), so the median is the average of the 5th and 6th numbers:
Median: \( \frac{86 + 86}{2} = 86 \)
Now, if the lowest score (35) is removed, the new set of scores becomes:
New arranged scores: \( 80, 82, 83, 86, 86, 86, 87, 89, 90 \)
New median with 9 scores:
New median: \( 86 \) (5th score, since it's an odd number of scores)
As observed, the median does not change when the lowest score is removed.
### Mode:
The mode is the most frequently occurring value in the data set.
In our set, the mode is \( 86 \) because it appears the most (3 times).
If the lowest score (35) is removed, the mode remains \( 86 \).
### Conclusion:
The mean includes all the values, so it is significantly affected by the lowest score. The median and mode are more resistant to changes from outliers.
Therefore, the correct answer is:
C) the mean
### Mean:
The mean (average) is calculated by summing all the scores and dividing by the number of scores.
Given scores: \( 82, 83, 80, 89, 86, 35, 86, 90, 86, 87 \)
Sum of scores: \( 82 + 83 + 80 + 89 + 86 + 35 + 86 + 90 + 86 + 87 = 804 \)
Number of scores: \( 10 \)
Mean: \( \frac{804}{10} = 80.4 \)
If the lowest score (35) were removed, the sum would be:
New sum: \( 804 - 35 = 769 \)
New mean without the lowest score: \( \frac{769}{9} \approx 85.44 \)
You can see that the mean changes significantly when the lowest score (35) is removed.
### Median:
The median is the middle value in a list when the numbers are arranged in ascending order.
Arranged scores: \( 35, 80, 82, 83, 86, 86, 86, 87, 89, 90 \)
Here, we have an even number of scores (10), so the median is the average of the 5th and 6th numbers:
Median: \( \frac{86 + 86}{2} = 86 \)
Now, if the lowest score (35) is removed, the new set of scores becomes:
New arranged scores: \( 80, 82, 83, 86, 86, 86, 87, 89, 90 \)
New median with 9 scores:
New median: \( 86 \) (5th score, since it's an odd number of scores)
As observed, the median does not change when the lowest score is removed.
### Mode:
The mode is the most frequently occurring value in the data set.
In our set, the mode is \( 86 \) because it appears the most (3 times).
If the lowest score (35) is removed, the mode remains \( 86 \).
### Conclusion:
The mean includes all the values, so it is significantly affected by the lowest score. The median and mode are more resistant to changes from outliers.
Therefore, the correct answer is:
C) the mean
