Can someone show me how to calculate the inner quartile range for the data set given? { 72, 80, 80, 82, 88, 90, 96}. Thanks.

1. arrange the numbers in ascending numerical order:

{ 72, 80, 80, 82, 88, 90, 96}.
2. Find the median, which is the middle number of the list. In the given case, the middle number of 7 number is the fourth, namely 82.
{ 72, 80, 80, 82, 88, 90, 96}
3. Find the first quartile:
Disregard the median and numbers higher than the median. For the remaining numbers, repeat step number 2, this is the first quartile. (80)
{ 72, 80, 80 ...}.
4. Find the third quartile: repeat step 3 using the upper half of the list of numbers.
{ ... 88, 90, 96}.
5. We should end up with the data set as follows:
{ 72, 80, 80, 82, 88, 90, 96}.
The inner quartile range is the difference between the third and the fisrt quartiles, namely 90-80=10 in the given case.

Note that there are specific procedures for finding the median when there the number of numbers is even.

Thank you.

Certainly! To calculate the inner quartile range (IQR) for a given data set, you need to perform the following steps:

Step 1: Sort the data in ascending order:

{ 72, 80, 80, 82, 88, 90, 96}

Sorting the data gives:

{72, 80, 80, 82, 88, 90, 96}

Step 2: Calculate the first quartile (Q1) and third quartile (Q3):

Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

In our example, the lower half is {72, 80, 80} and the upper half is {88, 90, 96}.

For the lower half:
- Count the number of values, which is 3.
- Since the number of values is odd, the median will be the middle value, which is 80.

For the upper half:
- Count the number of values, which is 3.
- Since the number of values is odd, the median will be the middle value, which is 90.

So, Q1 = 80 and Q3 = 90.

Step 3: Calculate the IQR:
IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

In our example, IQR = Q3 - Q1 = 90 - 80 = 10.

Therefore, the inner quartile range (IQR) for the given data set {72, 80, 80, 82, 88, 90, 96} is 10.