Interquartile Range Worksheet

Interquartile Range Deep Dive

Read each question carefully and provide accurate answers. Show all your work for calculations.

1. Explain in your own words what the first quartile (Q1), second quartile (Q2), and third quartile (Q3) represent in a data set.

2. For the data set: 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38, 40 a. The median (Q2) is  . b. The first quartile (Q1) is  . c. The third quartile (Q3) is  . d. The Interquartile Range (IQR) is  .

3. Consider the data set: 5, 8, 10, 12, 15, 18, 20, 22, 45. a. Calculate the IQR for this data set. b. Determine if there are any outliers using the 1.5 * IQR rule.

4. The box plot below shows the distribution of test scores for a math class. Use the box plot to answer the following questions.

a. What is the median score?   b. What is the range of the middle 50% of scores?   c. What is the lowest score (excluding outliers)?   d. What is the highest score (excluding outliers)?  

5. Two different brands of batteries were tested for their lifespan (in hours). Here are the results: Brand A: 10, 12, 15, 18, 20, 22, 25, 28, 30 Brand B: 5, 10, 15, 20, 25, 30, 35, 40, 45 Calculate the IQR for both brands. Which brand has a more consistent lifespan? Justify your answer.