Let's go through the steps to find the correct answer to the question regarding Norberto's scores.
First, we list Norberto's scores: 88, 81, 93, 85, and 98.
### Step 1: Calculate the Mean
The mean is the average of the scores. To find the mean:
1. Add all the scores together: [tex]\(88 + 81 + 93 + 85 + 98 = 445\)[/tex]
2. Divide the total by the number of scores: [tex]\( \frac{445}{5} = 89 \)[/tex]
So, the mean of the scores is 89.
### Step 2: Calculate the Median
The median is the middle number when the scores are arranged in ascending order.
First, we sort the scores: 81, 85, 88, 93, 98
Since there is an odd number of scores (5), the median is the middle one:
- The middle score after sorting is 88 (the third score in the sorted list).
So, the median of the scores is 88.
### Evaluating the Statements:
1. "The mode of the set of scores is 88."
- The mode is the number that appears most frequently. Since each score appears only once, there is no mode in this set.
2. "The median of the set of scores is 93."
- We calculated and found that the median is 88, not 93.
3. "The mean of this set of scores is larger than the median."
- We found the mean is 89, and the median is 88. Therefore, the mean is indeed larger than the median.
4. "The mean of the set is less than the median."
- This statement is false because the mean (89) is greater than the median (88).
So, the correct statement is:
- "The mean of this set of scores is larger than the median."
