A spa wants to determine which duration of its massage packages is the most popular. The spa has 30-minute, 50-minute, and 75-minute sessions. Which statistical measure should be used and is less affected by outliers and skewed data?
Mode is the most appropriate statistical measure for determining the popularity of massage package durations.
The mode indicates the most frequently occurring value in a data set, making it ideal for identifying which duration of massage sessions is the most popular. It is particularly useful when the data may be skewed or contain outliers, as it focuses solely on the frequency of occurrences rather than the numerical values themselves.
The mode is the best choice for this question because it identifies the massage duration that is most frequently booked, which directly answers the spa's query about popularity. Since the mode is not influenced by extreme values or the overall distribution of the data, it provides a clear and straightforward representation of client preferences.
While the median is useful for understanding the midpoint of a data set and is less affected by outliers than the mean, it does not specifically indicate which duration is the most popular. Instead, it reflects the central tendency of the data, which may not provide the necessary insight into the most frequently chosen massage length.
Standard deviation measures the variability or dispersion of data points around the mean. However, it does not indicate which duration is most popular. In this context, standard deviation is irrelevant because the spa is not looking to analyze the spread of durations, but rather to identify the most frequently selected option.
The mean calculates the average duration of the massage sessions booked, which can be skewed by outliers or extreme values, making it a poor choice for determining popularity. Since the mean may not reflect the most common duration chosen by clients, it does not serve the spa's purpose effectively.
To determine the most popular massage package duration, the mode is the appropriate statistical measure as it directly indicates the most frequently chosen option. The median, standard deviation, and mean each provide different types of information that do not specifically answer the spa's question about frequency and popularity, particularly in the presence of skewed data or outliers.
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