Sure, let’s analyze Max’s test scores step-by-step to find the mean, median, and mode of the data set. The scores are: 85, 93, 78, 90, 88, 97, and 88.
### 1. Calculating the Mean
The mean is the average of all the scores. To calculate the mean:
1. Add up all the test scores.
2. Divide the sum by the total number of test scores.
The test scores are: 85, 93, 78, 90, 88, 97, and 88.
1. Sum of the scores:
[tex]\[ 85 + 93 + 78 + 90 + 88 + 97 + 88 = 619 \][/tex]
2. Number of test scores:
[tex]\[ 7 \][/tex]
3. Mean:
[tex]\[ \frac{619}{7} \approx 88.42857142857143 \][/tex]
Thus, the mean score is approximately [tex]\( 88.43 \)[/tex].
### 2. Calculating the Median
The median is the middle value when the scores are arranged in ascending order.
1. First, arrange the scores in ascending order:
[tex]\[ 78, 85, 88, 88, 90, 93, 97 \][/tex]
2. Since there are 7 scores, the middle score is the 4th score in this ordered list:
[tex]\[ \text{Median} = 88 \][/tex]
Thus, the median score is [tex]\( 88 \)[/tex].
### 3. Calculating the Mode
The mode is the score that appears most frequently in the data set.
1. From the list of scores: 85, 93, 78, 90, 88, 97, and 88,
2. The score 88 appears twice, while all the other scores appear only once.
Thus, the mode score is [tex]\( 88 \)[/tex].
### Summary
- Mean: [tex]\( 88.43 \)[/tex]
- Median: [tex]\( 88 \)[/tex]
- Mode: [tex]\( 88 \)[/tex]
These values provide a comprehensive understanding of Max's performance on his biology tests.
