Question

which lists the steps in the correct order to find the median of this data set?
24, 16, 23, 30, 18, 29

1. put the numbers in order.
2. cross off high/low pairs.
3. add the leftover numbers.
4. divide the sum by 2.
5. put the numbers in order.
6. cross of high/low pairs.
7. cross off high/low pairs.
8. add the leftover numbers.
9. divide the sum by 2.
10. cross of high/low pairs.

Explanation:

Step1: Sort the data set

First, we need to put the numbers in order. For the data set \(24, 16, 23, 30, 18, 29\), the sorted order is \(16, 18, 23, 24, 29, 30\).

Step2: Cross - off high/low pairs

Cross off the highest and lowest numbers successively. Cross off \(16\) and \(30\), then \(18\) and \(29\). We are left with \(23\) and \(24\).

Step3: Calculate the median for the remaining two numbers

Since there are two numbers left (\(n = 2\) which is an even number of data points), we use the formula for the median of an even - numbered data set. The formula for the median of \(x_1,x_2\) (where \(x_1\leq x_2\)) is \(\frac{x_1 + x_2}{2}\). Here \(x_1=23\) and \(x_2 = 24\), so we add the leftover numbers (\(23+24\)) and divide the sum by \(2\).

Answer:

1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.