What are half of the observations always greater than?
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A. B. C. D. E.A
By definition, the median is the middle point. It divides the observations into two. The mean is NOT the answer because it may be affected by extreme values.
In this question, you are asked to identify what quantity is always greater than half of the observations. Let's analyze each answer choice to determine the correct option:
A. Median: The median is the middle value in a dataset when it is arranged in ascending or descending order. Half of the observations are greater than the median, and half are smaller. Therefore, the statement "half of the observations are always greater than the median" is incorrect.
B. Geometric mean: The geometric mean is the average of a set of numbers obtained by multiplying them together and then taking the nth root, where n is the number of values. Since the geometric mean involves multiplication, it is not guaranteed that half of the observations will be greater than it. Thus, the statement "half of the observations are always greater than the geometric mean" is incorrect.
C. None of these answers: This option suggests that none of the given answer choices are correct. However, we should continue analyzing the remaining options before concluding.
D. Mode: The mode is the value that appears most frequently in a dataset. There can be multiple modes or no mode at all. It is not necessarily true that half of the observations are greater than the mode. Hence, the statement "half of the observations are always greater than the mode" is incorrect.
E. Mean: The mean, also known as the average, is calculated by summing up all the values in a dataset and dividing by the number of observations. Since the mean considers all the values and their magnitudes, it is not guaranteed that half of the observations will be greater than the mean. Therefore, the statement "half of the observations are always greater than the mean" is incorrect.
After analyzing all the options, we find that none of the provided answer choices accurately represents a quantity that is always greater than half of the observations. Thus, the correct answer is option C: None of these answers.