When using statistics to evaluate a set of numbers the median:

Question

BlackTom AI · Accepted Answer

When evaluating a data set with statistics, the question points to the concept of the median and its defining property.
Option: The geometric average
This is a different measure of central tendency (the geometric mean), not the median. It involves multiplying values and taking roots, which is unrelated to the definition of median. Therefore this statement is incorrect.
Option: The average
Commonly, people refer to the average as the mean. The median is a distinct measure from the mean; they can be the same in symmetric distributions but are generally different. This option confuses two different central tendency concepts, making it inaccurate as a general definition of the median.
Option: Is a number with equal number of data points grater and less than it
This aligns with the formal definition of the median in a data set: the middle value that splits the ordered data so that half the observations are at or below it and half are at or above it. In a data set with an odd number of observations, it is the exact middle value; with an even number, it is commonly defined as the average of the two central values, but it still serves as a central point around which half the data lie on each side. This statement captures the core concept of the median, making it the correct interpretation in standard contexts.
Option: Is likely to change significantly in response to extraordinary values
This describes a property more associated with the mean, which can be pulled toward extreme values (outliers). The median is more resistant to outliers and does not typically change drastically with extraordinary values, unlike the mean. Hence, this statement is misleading about the median's behavior.

R E 411 B Quiz #3 practice

When using statistics to evaluate a set of numbers the median:

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