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Answer :
To calculate the arithmetic mean of the data set, sum all the numbers and divide by the total count (48.63). The median is found by ordering the data and averaging the middle values (48.6). The mode is the most frequently occurring number in the data set (66.9).
The student asked how to find the arithmetic mean, the median, and the mode of a given data set. The data set provided is 34.4, 66.9, 23.4, 57.2, 31.4, 66.9, 48.2, 42.0, 49.0, and 66.9.
To calculate the mean, we add all the numbers together and divide by the number of values in the data set:
- Sum of the data set = 34.4 + 66.9 + 23.4 + 57.2 + 31.4 + 66.9 + 48.2 + 42.0 + 49.0 + 66.9 = 486.3
- Number of values in the data set = 10
- Arithmetic mean = Sum of the data set / Number of values = 486.3 / 10 = 48.63
To find the median, we first arrange the data set in ascending order and then locate the central number:
- Ordered data set: 23.4, 31.4, 34.4, 42.0, 48.2, 49.0, 57.2, 66.9, 66.9, 66.9
- Since there are 10 values, the median will be the average of the 5th and 6th numbers, which are 48.2 and 49.0.
- Median = (48.2 + 49.0) / 2 = 48.6
The mode is the number that appears most frequently in the data set. In this case, 66.9 appears three times, making it the mode.
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