Can someone explain this question? For a set of scores, will the interquartile range always be less than the range? Explain your answer with an example.

My answer would be yes the interquartile will always be less than the range.Is this correct?
But I don't know of an example to show. Thanks.

yes. Make up an example.

Thank you. I managed to come up with an example.

Your answer is correct! The interquartile range will always be less than the range for a set of scores. Let me explain why.

First, let's understand what the range and interquartile range represent:

- Range: The range is a measure of the spread or dispersion of a data set. It is calculated by subtracting the minimum value from the maximum value in the set of scores. The range considers all the values in the data set.
- Interquartile Range (IQR): The interquartile range is a measure of the spread of the middle 50% of the data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The interquartile range only considers the middle 50% of the values, ignoring outliers.

To illustrate this with an example, let's consider the following set of scores: 10, 12, 14, 15, 16, 20, 22, 25, 60, 75.

To calculate the range, we subtract the minimum (10) from the maximum (75):
Range = 75 - 10 = 65

To find the interquartile range, we need to find the first quartile (Q1) and the third quartile (Q3). First, let's arrange the scores in ascending order: 10, 12, 14, 15, 16, 20, 22, 25, 60, 75.

- Q1: The median of the lower half of the scores. In this case, Q1 is the median of the values 10, 12, 14, and 15. The median of these values is 13.
- Q3: The median of the upper half of the scores. In this case, Q3 is the median of the values 20, 22, 25, 60, and 75. The median of these values is 25.

Now, we can calculate the interquartile range by subtracting Q1 from Q3:
IQR = 25 - 13 = 12

As you can see, the interquartile range (12) is less than the range (65) in this example.

Therefore, your answer is correct: the interquartile range will always be less than the range for a set of scores.