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The mean, or average, is a fundamental concept in statistics. To calculate the mean, you simply add up all the values in a dataset and then divide by the number of values in that set.
In the context of our problem, the dataset represents the number of miles employees travel using public transportation per day. For this group of 10 employees, the miles are added up to make 74.
To find the mean, divide this total by the number of employees: \[ \text{Mean} = \frac{74}{10} = 7.4 \text{ miles per day} \] With the introduction of a new employee traveling 90 miles, the new sum becomes 164, resulting in: \[ \text{New Mean} = \frac{164}{11} \approx 14.91 \text{ miles per day} \] The increase in mean highlights how sensitive it is to high-value data entries, illustrating that outliers can significantly shift the mean value.

The median provides the middle value in a dataset when organized in ascending order. It's a measure of central tendency often used to understand the midpoint of data. For our dataset of 10 values, after sorting, we find the middle position to be between the 5th and 6th values, both being 0: \[ \text{Median} = \frac{0 + 0}{2} = 0 \] After adding the new employee's data, the dataset becomes 11 values long. Thus, we simply take the 6th value in the ordered list for the median: 0. The median remains unaffected by the addition of the new employee's 90-mile travel figure, as it focuses on the middle value rather than the extremes. This robustness against outliers makes it a preferred measure in skewed distributions.

The mode is the value that occurs most frequently in a dataset. It's a straightforward measure of central tendency that's useful for categorical data or datasets with repeated values.
In our case, the number '0' appears the most, occurring multiple times: in all, seven times.
This makes '0' the mode. Being the most popular data point, the mode effectively represents the most common outcome for this particular dataset of employee transportation miles.

An outlier is a data value that significantly differs from the other values in a dataset. It can skew data-driven analysis and results.
In our data, the initial dataset has a mileage range from 0 to 60. Introducing the employee traveling 90 miles dramatically impacts some statistical measures. Notably, the outlier increased the mean from 7.4 to approximately 14.91, emphasizing its influence on data that relies on the average calculation.
However, concentrating on median and mode helped strip away the distortions caused by outliers. Thus, recognizing outliers helps ensure data interpretations are accurate and reliable.

Data analysis involves thorough examination of a dataset to extract meaningful insights. For the exercise at hand, we're examining employee travel distance using public transport.
Through calculations of mean, median, and mode, and understanding the impact of outliers, we gain a clearer picture of the dataset. Each statistical measure reveals different insights about the dataset. While mean gives an overall average, the median provides a resistant central point, and the mode shows commonality.
Recognizing outliers and their effects helps refine these insights, allowing better strategic decisions, like promoting public transport to reduce inefficient vehicle use amongst employees. This comprehensive analysis leads to more informed decisions about resource management and company policies.