Question

what is the median of the following numbers?
1, 2, 10, 6, 4, 4, 6, 3, 1, 4

Explanation:

Step1: Order the numbers

First, we need to sort the given numbers in ascending order. The numbers are \(1, 2, 10, 6, 4, 4, 6, 3, 1, 4\). When we sort them, we get: \(1, 1, 2, 3, 4, 4, 4, 6, 6, 10\).

Step2: Find the middle value(s)

There are \(n = 10\) numbers, which is an even count. For an even number of values, the median is the average of the two middle numbers. The middle numbers are the \(\frac{n}{2}\)-th and \((\frac{n}{2}+ 1)\)-th values. Here, \(\frac{10}{2}=5\)-th and \((\frac{10}{2}+ 1)=6\)-th values.

Looking at the sorted list: the 5th value is \(4\) and the 6th value is also \(4\).

Step3: Calculate the median

To find the median, we take the average of these two middle numbers. The formula for the median when \(n\) is even is \(\text{Median}=\frac{\text{Value at } \frac{n}{2} + \text{Value at } (\frac{n}{2}+ 1)}{2}\). Substituting the values, we get \(\frac{4 + 4}{2}=\frac{8}{2}=4\).

Answer:

\(4\)