Answer :
Final Answer:
The arithmetic mean of the given data set is 38.76.
Explanation:
The arithmetic mean, commonly referred to as the average, is calculated by adding up all the values in a data set and then dividing by the total number of values. In this case, the sum of the values in the data set is 386.7 (34.6 + 54.6 + 29.5 + 12.2 + 47.1 + 37.2 + 54.6 + 38.6 + 24.4 + 54.6), and there are 10 values in the data set. When we divide the sum by the total number of values (10), we get the arithmetic mean: 386.7 / 10 = 38.67.
To further clarify, the arithmetic mean represents a central tendency of the data set, providing a sense of its typical value. It is important to note that the arithmetic mean can be influenced by outliers, which are values that significantly deviate from the rest of the data. In this data set, the value 54.6 appears three times, which contributes to a relatively higher mean compared to the other values.
In summary, the arithmetic mean of the given data set is 38.76, which is obtained by dividing the sum of all values by the total number of values. This value gives us an idea of the typical magnitude within the data set.
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