Question

For the following set of scores of a continuous variable: 33, 14, 10, 9, 16, 8, 11, 13, 20 : A. What is the range? (show calculation) B. Identify the interquartile range. Write your answer to the following steps. Note: Although later chapters discuss IQR as well, you only need knowledge from Chapter 4 for this question. Step 1: Write down the set of scores from smallest to largest: Step 2: What are the values for the first quartile (Q1) and the third quartile (Q3) in this continuous set of scores? (Hint: You may use the Quartile location formula in the Boxplot tutorial in the Lab 2 folder to help work on this question). Step 3: Calculate the interquartile range (show calculation)

Answer 1

The range of the set of scores is 25. The scores are rearranged in ascending order to identify the interquartile range (IQR). Q1 is 9.5 and Q3 is 18. The IQR, which is the difference between Q3 and Q1, is 8.5.

Step-by-step explanation:

For the following set of scores of a continuous variable: 33, 14, 10, 9, 16, 8, 11, 13, 20:

A. The range is the difference between the highest and the lowest score. Here, Range = Highest score - Lowest score = 33 - 8 = 25.

B. To identify the interquartile range (IQR), we need to follow these steps:

1. First, rearrange the scores from smallest to largest: 8, 9, 10, 11, 13, 14, 16, 20, 33
2. Second, find Q1 and Q3. Q1 is the median of the lower half of the data (not including the median of the whole data set if it's part of the data). Here, Q1 is the median of the numbers 8, 9, 10, 11. We find this by averaging the two middle numbers, 9 and 10, and get 9.5. Q3 is the median of the higher half of the data, which in this case is the median of 14, 16, 20, 33. By averaging 16 and 20, we get 18.
3. Lastly, calculate the IQR. IQR = Q3 - Q1 = 18 - 9.5 = 8.5.

Learn more about Range and Interquartile Range