To tackle this question, we need to closely scrutinize the given data regarding the time it took for seven different gorillas to adapt and interact regularly in their new habitat. The measured times (in days) are:
- Gorilla 1: 2.5 days
- Gorilla 2: 3.1 days
- Gorilla 3: 8.3 days
- Gorilla 4: 3.3 days
- Gorilla 5: 2.7 days
- Gorilla 6: 3.2 days
- Gorilla 7: 3.4 days
We need to determine if the data is reliable by analyzing possible outliers. Here is a step-by-step guide:
1. Calculate the Mean (Average) Time:
The mean is obtained by summing up all the time measurements and dividing by the number of measurements.
Mean time = [tex]\( \frac{2.5 + 3.1 + 8.3 + 3.3 + 2.7 + 3.2 + 3.4}{7} \)[/tex].
2. Compute the Standard Deviation (Measure of Data Dispersion):
The standard deviation offers insight into how spread out the times are around the mean. It's calculated as the square root of the average squared differences from the mean:
[tex]\[
\sigma = \sqrt{\frac{\sum (X_i - \bar{X})^2}{N}},
\][/tex]
where [tex]\(X_i\)[/tex] represents each measured time, [tex]\( \bar{X} \)[/tex] is the mean time, and [tex]\( N \)[/tex] is the number of measurements.
3. Determine the Outlier Threshold:
Typically, data points are considered outliers if they fall outside the range:
[tex]\[
\bar{X} \pm 2\sigma,
\][/tex]
where [tex]\( \bar{X} \)[/tex] is the mean and [tex]\( \sigma \)[/tex] is the standard deviation.
4. Identify the Outliers:
Compare each time measurement with the calculated lower and upper thresholds.
5. Analyze the Data:
- If there are any time measurements that fall outside of these thresholds, those will be considered outliers.
- If there is at least one outlier, the presence of such points may suggest that the data may not be reliable because the outlier(s) indicate an inconsistency in the time measurements.
Given the analysis:
- The calculated values indicate that there is one clear outlier in the dataset.
- The mean and standard deviation computations would support identifying the time [tex]\(8.3\)[/tex] days as distinctively different from the rest of the times which lie around [tex]\(2.5\)[/tex] to [tex]\(3.4\)[/tex] days.
Conclusion:
Given that there is an outlier in the dataset, the data may not be considered entirely reliable.
Therefore, the correct answer is:
C. The data may not be reliable because there is an outlier.
