Answer :
Final answer:
After calculating, none of the provided answer options are correct. The correct mean, median, and mode for the data set are 77.2, 82.5, and 82, respectively. Considering the data set does not have outliers, the mean would be the best measure of center for this data set, although it was not an option provided.
Explanation:
To find the mean, median, and mode of the data set 36, 82, 94, 83, 86, 82, you calculate them as follows:
- Mean: Add all the numbers together and divide by the count of the numbers. So, (36 + 82 + 94 + 83 + 86 + 82) / 6 = 463 / 6 = 77.2.
- Median: First, order the numbers from least to greatest. The ordered set is 36, 82, 82, 83, 86, 94. Because there is an even number of values, take the average of the middle two numbers. Thus, the median is (82 + 83) / 2 = 82.5.
- Mode: The number that appears most frequently, which is 82.
From these calculations, it is clear that none of the provided answer options (a, b, c, or d) are correct. Instead, the correct calculations are: Mean: 77.2, Median: 82.5, Mode: 82. To determine which measure of center best represents the data, consider the distribution of values. If there are no clear outliers, the mean might represent the data set well. However, if there are outliers, the median could be more representative. The mode is generally less used as a measure of center unless the data is categorical.
