Question

find the median for the following group of data items
91, 96, 99, 97, 92, 96
the median is □. (type an integer or a decimal.)

Explanation:

Step1: Sort the data

First, we sort the given data set: 91, 92, 96, 96, 97, 99. Wait, wait, the original data is 91, 96, 99, 97, 92, 96. Let's sort them in ascending order: 91, 92, 96, 96, 97, 99. Wait, no, let's list all numbers: 91, 96, 99, 97, 92, 96. Let's sort correctly: 91, 92, 96, 96, 97, 99. Wait, the number of data points is 6 (even number). The median for an even number of data points is the average of the two middle numbers.

Step2: Find the middle positions

For \( n = 6 \) (number of data points), the middle positions are \( \frac{n}{2}=3 \) and \( \frac{n}{2}+ 1=4 \). So the 3rd and 4th numbers in the sorted list. The sorted list is [91, 92, 96, 96, 97, 99]. The 3rd number is 96 and the 4th number is 96.

Step3: Calculate the median

The median is the average of these two numbers: \( \frac{96 + 96}{2}=\frac{192}{2}=96 \). Wait, wait, wait, did I sort correctly? Let's re - sort the original data: 91, 92, 96, 96, 97, 99? Wait, original data: 91, 96, 99, 97, 92, 96. Let's sort step by step:

• Start with 91.
• Then 92 (since 92>91).
• Then 96 (96>92).
• Then another 96 (equal to 96).
• Then 97 (97>96).
• Then 99 (99>97). So sorted list: 91, 92, 96, 96, 97, 99. Number of elements \( n = 6 \). Middle terms are at positions 3 and 4. Position 3: 96, position 4: 96. Median \(=\frac{96 + 96}{2}=96\). Wait, but wait, maybe I made a mistake in the number of elements. Let's count the original data: 91, 96, 99, 97, 92, 96. That's 6 numbers. So sorted: 91, 92, 96, 96, 97, 99. So middle two are 96 and 96. Average is \( \frac{96+96}{2}=96 \).

Wait, another way: Let's list all numbers: 91, 92, 96, 96, 97, 99. Wait, no, 91, 92, 96, 96, 97, 99? Wait, 91, 92, 96, 96, 97, 99. So the two middle numbers are 96 and 96. So median is 96.

Wait, but let's check again. Original data: 91, 96, 99, 97, 92, 96. Let's sort:

91, 92, 96, 96, 97, 99. Yes. So n = 6. Middle terms: 3rd and 4th. 3rd: 96, 4th: 96. Median: (96 + 96)/2=96.

Answer:

96