Question

The numbers of trading cards owned by 10 middle-school students are given below.
(Note that these are already ordered from least to greatest.)369, 381, 393, 432, 454, 514, 529, 560, 593, 665
Suppose that the number 369 from this list changes to 429. Answer the following.
What happens to the median?

Answer 1

To find the median of a set of numbers, you first need to determine the middle values. For a list with an even number of entries, the median is the average of the two middle numbers.

Initially, the numbers of trading cards are:
369, 381, 393, 432, 454, 514, 529, 560, 593, 665

With 10 values, the median is the average of the 5th and 6th numbers:
- 5th number: 454
- 6th number: 514

So the median is:
\[
\text{Median} = \frac{454 + 514}{2} = \frac{968}{2} = 484
\]

Now, we replace 369 with 429, and the new set of numbers becomes:
429, 381, 393, 432, 454, 514, 529, 560, 593, 665

Again, this has 10 values, so we will find the median using the 5th and 6th numbers in the new ordered list:
- 5th number: 454
- 6th number: 514

The median remains the same:
\[
\text{Median} = \frac{454 + 514}{2} = \frac{968}{2} = 484
\]

In conclusion, the median does not change when 369 is replaced with 429; it remains 484.