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
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
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 calculate Derrick's mean and median test scores, we'll follow the steps below:
### Mean Test Score:
The mean is calculated by adding all the test scores together and then dividing by the number of scores.
1. **Sum of Scores**:
\( 25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 734 \)
2. **Number of Scores**:
There are 10 scores.
3. **Mean Calculation**:
\[
\text{Mean} = \frac{\text{Total Sum of Scores}}{\text{Number of Scores}} = \frac{734}{10} = 73.4
\]
### Median Test Score:
The median is the middle value when the numbers are arranged in order. If there is an even number of observations, as in this case, the median is the average of the two middle numbers.
1. **Arrange the Scores in Order**:
\( 25, 40, 68, 70, 78, 85, 85, 95, 98, 100 \)
2. **Find the Middle Values**:
Since there are 10 scores, the middle values are the 5th and 6th scores:
- 5th score: 78
- 6th score: 85
3. **Median Calculation**:
\[
\text{Median} = \frac{78 + 85}{2} = \frac{163}{2} = 81.5
\]
### Summary of Results:
- **Mean Test Score**: 73.4
- **Median Test Score**: 81.5
### Which Gives a Better Picture of His Scores?
The median is often a better representation of a typical score when dealing with a set of numbers that may have outliers or skewness. In Derrick's case, the mean is influenced by the higher scores (e.g., the 100), which may not reflect his overall performance as accurately as the median.
Thus, the **median (81.5)** gives a better picture of Derrick's scores than the mean (73.4).
### Mean Test Score:
The mean is calculated by adding all the test scores together and then dividing by the number of scores.
1. **Sum of Scores**:
\( 25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 25 + 40 + 68 + 85 + 95 + 98 + 70 + 78 + 85 + 100 = 734 \)
2. **Number of Scores**:
There are 10 scores.
3. **Mean Calculation**:
\[
\text{Mean} = \frac{\text{Total Sum of Scores}}{\text{Number of Scores}} = \frac{734}{10} = 73.4
\]
### Median Test Score:
The median is the middle value when the numbers are arranged in order. If there is an even number of observations, as in this case, the median is the average of the two middle numbers.
1. **Arrange the Scores in Order**:
\( 25, 40, 68, 70, 78, 85, 85, 95, 98, 100 \)
2. **Find the Middle Values**:
Since there are 10 scores, the middle values are the 5th and 6th scores:
- 5th score: 78
- 6th score: 85
3. **Median Calculation**:
\[
\text{Median} = \frac{78 + 85}{2} = \frac{163}{2} = 81.5
\]
### Summary of Results:
- **Mean Test Score**: 73.4
- **Median Test Score**: 81.5
### Which Gives a Better Picture of His Scores?
The median is often a better representation of a typical score when dealing with a set of numbers that may have outliers or skewness. In Derrick's case, the mean is influenced by the higher scores (e.g., the 100), which may not reflect his overall performance as accurately as the median.
Thus, the **median (81.5)** gives a better picture of Derrick's scores than the mean (73.4).