To determine the effect on the median when excluding an outlier from the dataset {510, 12, 14, 1824, 60}, we first need to identify the outlier and then calculate the median before and after its exclusion.
Step 1: Identify the outlier
In the dataset {510, 12, 14, 1824, 60}, it is clear that 1824 is an outlier, as it is significantly higher than the other numbers.
Step 2: Calculate the median before exclusion
To find the median, we need to sort the numbers in ascending order:
- Sorted dataset: {12, 14, 60, 510, 1824}
The median of a dataset with an odd number of elements is the middle number. In this case, the middle number (3rd number in the sorted set) is 60.
Step 3: Exclude the outlier and find the new median
Now we exclude the outlier (1824):
- New dataset: {12, 14, 60, 510}
Next, we sort the new dataset (although it is already sorted):
- Sorted new dataset: {12, 14, 60, 510}
Now, we calculate the median of this even-sized dataset. For a dataset with an even number of elements, the median is the average of the two middle numbers (2nd and 3rd).
- The two middle numbers are 14 and 60.
- Median = (14 + 60) / 2 = 74 / 2 = 37.
Summary
- Original median (with outlier): 60
- New median (without outlier): 37
Conclusion
Excluding the outlier 1824 results in a decrease in the median from 60 to 37. So, the effect on the median is a decrease.
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