To analyze the data you provided (18, 19, 21, 22, 19, 56, 20) and determine the best measure of the center (mean or median), let's first identify the outlier and then calculate both the mean and median.
Step 1: Identify the Outlier
The values in the dataset are:
- 18
- 19
- 21
- 22
- 19
- 56 (potential outlier)
- 20
In this case, the value 56 stands out significantly higher than the other values (the largest is 22). This suggests that 56 is an outlier.
Step 2: Calculate the Mean
To calculate the mean:
- Add all the values together.
- Divide by the total number of values.
Calculating the mean: \[ \text{Mean} = \frac{(18 + 19 + 21 + 22 + 19 + 56 + 20)}{7} = \frac{175}{7} = 25 \]
Step 3: Calculate the Median
To find the median, first, sort the data:
- Sorted list: 18, 19, 19, 20, 21, 22, 56
Since there are 7 observations (an odd number), the median is the middle value:
- Median = 20 (4th value in the sorted list)
Step 4: Comparing Mean and Median
- Mean with outlier: 25
- Median: 20
Conclusion
Since the outlier (56) significantly raises the mean compared to the median, the mean is affected by the outlier while the median remains a more stable measure of center in this case.
Recommendation: The median is the better measure of center for this dataset, as it is not affected by the outlier.
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