Question
Derrick needs to figure out how he’s doing on his test scores so far this year. You can help by calculating the mean and the median to get an overall picture of his scores. Below are all of his scores:
25, 40, 68, 85, 95, 98, 70, 78, 85, 100
(3 points)
What is Derrick's mean test score so far?
What is Derrick's median test score so far?
Which gives a better picture of his scores?
25, 40, 68, 85, 95, 98, 70, 78, 85, 100
(3 points)
What is Derrick's mean test score so far?
What is Derrick's median test score so far?
Which gives a better picture of his scores?
Answers
GPT-4o mini
To help Derrick analyze his test scores, we will calculate the mean and the median.
### Derrick's Test Scores:
Scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100
#### Step 1: Calculate the Mean
The mean is calculated by adding all the scores together and dividing by the number of scores.
1. **Sum of Scores:**
\[
25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 834
\]
2. **Number of Scores:**
There are 10 scores.
3. **Mean Calculation:**
\[
\text{Mean} = \frac{\text{Sum of Scores}}{\text{Number of Scores}} = \frac{834}{10} = 83.4
\]
### Step 2: Calculate the Median
The median is the middle value of a dataset. To find the median, we first need to arrange the scores in ascending order:
**Sorted Scores:**
25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Since there is an even number of scores (10), the median will be the average of the two middle numbers (5th and 6th scores).
1. **Identifying the Middle Scores:**
- 5th score: 78
- 6th score: 85
2. **Median Calculation:**
\[
\text{Median} = \frac{78 + 85}{2} = \frac{163}{2} = 81.5
\]
### Summary of Calculations:
- **Mean test score:** 83.4
- **Median test score:** 81.5
### Which gives a better picture of his scores?
In this case, the mean (83.4) is slightly higher than the median (81.5). The mean can be influenced by extreme values (like the low score of 25), whereas the median provides a better measure of central tendency in the presence of outliers.
In summary:
- Given the presence of a low outlier (25), the **median** gives a better picture of Derrick's scores overall, as it reflects that most of his scores are much higher than 25.
### Derrick's Test Scores:
Scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100
#### Step 1: Calculate the Mean
The mean is calculated by adding all the scores together and dividing by the number of scores.
1. **Sum of Scores:**
\[
25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 834
\]
2. **Number of Scores:**
There are 10 scores.
3. **Mean Calculation:**
\[
\text{Mean} = \frac{\text{Sum of Scores}}{\text{Number of Scores}} = \frac{834}{10} = 83.4
\]
### Step 2: Calculate the Median
The median is the middle value of a dataset. To find the median, we first need to arrange the scores in ascending order:
**Sorted Scores:**
25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Since there is an even number of scores (10), the median will be the average of the two middle numbers (5th and 6th scores).
1. **Identifying the Middle Scores:**
- 5th score: 78
- 6th score: 85
2. **Median Calculation:**
\[
\text{Median} = \frac{78 + 85}{2} = \frac{163}{2} = 81.5
\]
### Summary of Calculations:
- **Mean test score:** 83.4
- **Median test score:** 81.5
### Which gives a better picture of his scores?
In this case, the mean (83.4) is slightly higher than the median (81.5). The mean can be influenced by extreme values (like the low score of 25), whereas the median provides a better measure of central tendency in the presence of outliers.
In summary:
- Given the presence of a low outlier (25), the **median** gives a better picture of Derrick's scores overall, as it reflects that most of his scores are much higher than 25.