To understand how the outlier affects the median, we first need to calculate the median of both data sets: one without the outlier and one with the outlier.
### Calculating the Median for the Data Without an Outlier
Data Set Without an Outlier:
[tex]\[ 108, 113, 105, 118, 124, 121, 109 \][/tex]
1. Arrange the numbers in ascending order:
[tex]\[ 105, 108, 109, 113, 118, 121, 124 \][/tex]
2. Since there are 7 numbers (an odd number of elements), the median is the middle number:
[tex]\[ \text{Median} = 113 \][/tex]
### Calculating the Median for the Data With an Outlier
Data Set With an Outlier:
[tex]\[ 108, 113, 105, 118, 124, 121, 109, 61 \][/tex]
1. Arrange the numbers in ascending order:
[tex]\[ 61, 105, 108, 109, 113, 118, 121, 124 \][/tex]
2. Since there are 8 numbers (an even number of elements), the median is the average of the two middle numbers:
- The two middle numbers are the 4th and 5th numbers:
[tex]\[ 109, 113 \][/tex]
- The median is:
[tex]\[ \text{Median} = \frac{109 + 113}{2} = \frac{222}{2} = 111 \][/tex]
### Comparing the Medians
- Median without the outlier: 113
- Median with the outlier: 111
### Conclusion
By comparing the results, we can see that the outlier:
1. Decreased the median from 113 to 111.
Thus, the correct answer is:
- The outlier slightly affected the median.
