Question

which of the following statements is false about the median?
data must be organized from least to greatest in order to determine the median.
the median is always the number in the middle of an organized data set.
the median always contains an equal number of data values below it as it does above it.
the median may be a number not contained in the original data set.

Explanation:

• For the first option: To find the median, data must be ordered (either least - to - greatest or greatest - to - least). So, this statement is true.
• For the second option: When the number of data points \(n\) is odd (\(n = 2k + 1,k\in\mathbb{Z}\)), the median is the \((k + 1)\) - th value in the ordered data set. But when \(n\) is even (\(n=2k,k\in\mathbb{Z}\)), the median is the average of the \(k\) - th and \((k + 1)\) - th values. So, it is not always the number in the middle of an organized data set.
• For the third option: By the definition of the median, in an ordered data set, the number of data values below the median is equal to the number of data values above the median (or differ by at most \(1\) when \(n\) is odd). So, this statement is true.
• For the fourth option: For example, if the data set is \(\{1,2,4,5\}\), \(n = 4\), the median is \(\frac{2 + 4}{2}=3\), which is not in the original data set. So, this statement is true.

Answer:

The median is always the number in the middle of an organized data set.