Given the lengths of the bacterial cells in the provided data, the scientists notice that the value of 85 micrometers significantly stands out compared to the other measurements, which are all around 4-5 micrometers. This suggests that the 85 micrometers value might be an outlier. Here's a step-by-step approach to deal with this situation logically:
1. Identify the Outlier:
Look at the data values: 4.3, 5.2, 85.0, 5.3, 4.8, 4.9, 4.8, 4.6, 4.3, 4.8. The value 85.0 is distinctly higher than the others, indicating it could be an outlier.
2. Calculate the Mean without the Outlier:
To calculate the mean length of the cells without considering the outlier value:
- First, exclude the outlier (85.0) from the data.
- The remaining lengths are: 4.3, 5.2, 5.3, 4.8, 4.9, 4.8, 4.6, 4.3, 4.8.
- Sum these lengths: [tex]\(4.3 + 5.2 + 5.3 + 4.8 + 4.9 + 4.8 + 4.6 + 4.3 + 4.8 = 43.0 \)[/tex] micrometers.
- Divide the sum by the number of values (9 in this case): [tex]\(\frac{43.0}{9} = \approx 4.777777777777778 \)[/tex] micrometers.
3. Interpret the Outlier's Impact:
The mean length without considering the outlier is approximately 4.78 micrometers, which is much closer to the range of the other measurements, suggesting that the outlier has a substantial impact on the data's average.
4. Decision on Handling the Outlier:
Considering the standard practices in dealing with outliers:
- If an outlier is vastly different from the rest of the data, it might indicate an error in measurement or a rare event.
- Reviewing lab notes or measurement processes for potential errors is crucial.
- If no error is found, it could be a rare instance; rechecking similar conditions or further data collection might help ensure accuracy.
Based on these considerations, the most reasonable approach would be:
- Consider that there was an error during measuring and collect further data.
This allows for verifying the accuracy of the measurements and ensures that conclusions drawn are based on reliable data.
