Question

A data set is given to be \([1, 2, 0, -1, -3, 1, 2, 0, 1]\).
The median of the data set is ____. (rounded off to the nearest integer)

Hint:

For an odd number of data points, sort them and pick the middle value at position (n+1)/2; no averaging is needed.

Answer 1

Correct Answer: 1

Step 1: Arrange the data in order.
The given data set is \(1, 2, 0, -1, -3, 1, 2, 0, 1\). This has \(9\) values. To find the median we first need to sort the data from smallest to largest. Sorting gives us:
\[ -3, -1, 0, 0, 1, 1, 1, 2, 2 \]

Step 2: Recall the rule for finding the median.
The median is the middle value of a sorted data set. When the number of observations \(n\) is odd, the median sits at position
\[ \frac{n+1}{2} \]
in the sorted list. Here \(n = 9\), which is odd, so we do not need to average two middle terms; there is a single middle term.

Step 3: Locate the middle position.
\[ \frac{n+1}{2} = \frac{9+1}{2} = 5 \]
So the median is the \(5^{th}\) value in the sorted list.

Step 4: Read off the value at that position.
Counting through the sorted list \(-3, -1, 0, 0, 1, 1, 1, 2, 2\): the \(1^{st}\) value is \(-3\), the \(2^{nd}\) is \(-1\), the \(3^{rd}\) is \(0\), the \(4^{th}\) is \(0\), and the \(5^{th}\) is \(1\).

Final Answer:
The median of the data set is
\[ \boxed{1} \]