While studying bacterial cells, scientists measure the lengths of the cells in one colony. The chart shows their data
| Cell number | Length (in micrometers) |
| ----------- | ----------------------- |
| 1 | 4.3 |
| 2 | 5.2 |
| 3 | 85.0 |
| 4 | 5.3 |
| 5 | 4.8 |
| 6 | 4.9 |
| 7 | 4.8 |
| 8 | 4.6 |
| 9 | 4.3 |
| 10 | 4.5 |
The scientists notice that one measurement stands out. How should the scientists best deal with this measurement?
A. Accept it as true and use 85 micrometers in the data when they find the average length.
B. Accept it as true but say that it is the only cell that has ever been that long.
C. Consider that there was an error during measuring and collect further data.
D. Consider that it is possible but very unlikely for these bacterial cells to be so long.
Answer (1)
The measurement 85.0 is much larger than other cell lengths, suggesting it might be an outlier.
Calculating the mean with the outlier (12.76) and without it (5.29) shows a significant difference, while the median remains stable at 4.8.
The outlier skews the average cell length, indicating a potential measurement error.
The scientists should consider a measurement error and collect more data to verify the initial measurement. consider that there was an error during measuring and collect further data
Explanation
Analyze the problem and data We are given a set of bacterial cell lengths: 4.3, 5.2, 85.0, 5.3, 4.8, 4.9, 4.8, 4.6, 4.3, 4.4 micrometers. Our task is to determine how scientists should best handle the unusually large measurement of 85.0 micrometers.
Identify the potential outlier The value 85.0 is significantly larger than the other values, which range from 4.3 to 5.3. This suggests that 85.0 might be an outlier, which could be due to a measurement error or a genuinely rare occurrence.
Calculate mean and median Let's calculate the mean and median of the data with and without the potential outlier to see how much it affects the central tendency.
With the outlier: Mean = 10 4.3 + 5.2 + 85.0 + 5.3 + 4.8 + 4.9 + 4.8 + 4.6 + 4.3 + 4.4 = 10 127.6 = 12.76 micrometers Median = 4.8 micrometers
Without the outlier: Mean = 9 4.3 + 5.2 + 5.3 + 4.8 + 4.9 + 4.8 + 4.6 + 4.3 + 4.4 = 9 47.6 ≈ 5.29 micrometers Median = 4.8 micrometers
Assess the impact of the outlier As we can see, the outlier significantly affects the mean, increasing it from approximately 5.29 to 12.76 micrometers. The median, however, remains unchanged at 4.8 micrometers. This indicates that the outlier skews the average cell length.
Determine the best course of action Given the significant impact of the outlier on the mean, it would be premature to accept it as a true value without further investigation. It is important to consider the possibility of a measurement error. The best course of action would be to consider that there was a potential error during measuring and collect further data to verify the measurement.
Final Answer Therefore, the scientists should consider that there was an error during measuring and collect further data.
Examples
In scientific research, identifying and handling outliers is crucial for accurate data analysis. For instance, in a clinical trial measuring drug effectiveness, an outlier patient's response could skew the overall results. Scientists must carefully investigate such outliers to determine if they represent a genuine effect, a measurement error, or a unique characteristic of that individual. Proper handling of outliers ensures that conclusions drawn from the data are reliable and valid, leading to better informed decisions and advancements in the field.
