Question

Alicia received the following seven scores on her math assignments.

80, 90, 10, 75, 90, 95, 99

Find the mean and median. Which measure of center best represents the data?
the mean
the median
both the mean and the median
neither the mean nor the median

Answer 1

To find the mean and median of Alicia's scores, we start with the given scores:

**Scores**: 80, 90, 10, 75, 90, 95, 99

### Calculating the Mean

The mean is calculated by summing all the scores and dividing by the total number of scores.

1. **Sum of the scores**:
\( 80 + 90 + 10 + 75 + 90 + 95 + 99 = 539 \)

2. **Number of scores**: 7

3. **Mean**:
\[
\text{Mean} = \frac{\text{Sum of scores}}{\text{Number of scores}} = \frac{539}{7} \approx 77
\]

### Calculating the Median

The median is the middle value when the scores are arranged in ascending order.

1. **Arrange the scores**:
\( 10, 75, 80, 90, 90, 95, 99 \)

2. **Finding the median**:
Since there are 7 scores (an odd number), the median is the 4th score in the ordered list.
\[
\text{Median} = 90
\]

### Summary of Results
- **Mean**: \( \approx 77 \)
- **Median**: \( 90 \)

### Determine Which Measure of Center Best Represents the Data

The mean is affected by extreme values (in this case, the score of 10), which drags the mean down. The median, however, represents the middle score and is less affected by outliers.

In this case, since the median (90) is significantly higher than the mean (approximately 77), the median is a better representation of Alicia's scores than the mean.

### Conclusion
The best measure of center that represents the data is **the median**.