Question
Students reported the amount of time (in minutes) that it takes them to travel to school in the morning.
Their responses are shown below in order from least to greatest.
10, 15, 15, 19, 25, 30, 34, 45
Suppose that the travel time of 10 minutes changes to 19 minutes. Answer the following.
(a) What happens to the range? (Choose one and fill in the blank if it’s there)
• The range increases by ___ minutes.
• The range decreases by ___ minutes.
• The range stays the same.
• The IQR increases by ___ minutes.
(b) What happens to the interquartile range (IQR)? (Pick and and fill in the blank if it’s there)
• The IQR decreases by ___ minutes.
O The IQR stays the same.
Their responses are shown below in order from least to greatest.
10, 15, 15, 19, 25, 30, 34, 45
Suppose that the travel time of 10 minutes changes to 19 minutes. Answer the following.
(a) What happens to the range? (Choose one and fill in the blank if it’s there)
• The range increases by ___ minutes.
• The range decreases by ___ minutes.
• The range stays the same.
• The IQR increases by ___ minutes.
(b) What happens to the interquartile range (IQR)? (Pick and and fill in the blank if it’s there)
• The IQR decreases by ___ minutes.
O The IQR stays the same.
Answers
Answered by
GPT-4o mini
To determine what happens to the range and interquartile range (IQR) when the travel time of 10 minutes changes to 19 minutes, we will first analyze the original and modified datasets.
**Original Data:**
10, 15, 15, 19, 25, 30, 34, 45
- **Minimum:** 10
- **Maximum:** 45
- **Range:** Maximum - Minimum = 45 - 10 = 35 minutes
**Modified Data:**
19, 15, 15, 19, 25, 30, 34, 45 (after replacing 10 with 19 and sorting)
- **Minimum:** 15
- **Maximum:** 45
- **Range:** Maximum - Minimum = 45 - 15 = 30 minutes
**(a) What happens to the range?**
The original range was 35 minutes, and the new range is 30 minutes.
- The range **decreases by 5 minutes.**
So the correct choice is:
• The range decreases by **5 minutes.**
---
**(b) What happens to the interquartile range (IQR)?**
To calculate the IQR for both the original and modified datasets, we need to find the first (Q1) and third (Q3) quartiles.
**Original Data:**
- Ordered: 10, 15, 15, 19, 25, 30, 34, 45
- Median (Q2): (19 + 25) / 2 = 22
- Q1: Median of the lower half (10, 15, 15, 19) = (15 + 15) / 2 = 15
- Q3: Median of the upper half (25, 30, 34, 45) = (30 + 34) / 2 = 32
- **IQR:** Q3 - Q1 = 32 - 15 = 17 minutes
**Modified Data:**
- Ordered: 15, 15, 19, 19, 25, 30, 34, 45
- Median (Q2): (19 + 25) / 2 = 22
- Q1: Median of the lower half (15, 15, 19, 19) = (15 + 19) / 2 = 17
- Q3: Median of the upper half (25, 30, 34, 45) = (30 + 34) / 2 = 32
- **IQR:** Q3 - Q1 = 32 - 17 = 15 minutes
So, the IQR changed from 17 minutes to 15 minutes.
**(b) What happens to the IQR?**
The IQR **decreases by 2 minutes.**
So the correct choice is:
• The IQR decreases by **2 minutes.**
**Original Data:**
10, 15, 15, 19, 25, 30, 34, 45
- **Minimum:** 10
- **Maximum:** 45
- **Range:** Maximum - Minimum = 45 - 10 = 35 minutes
**Modified Data:**
19, 15, 15, 19, 25, 30, 34, 45 (after replacing 10 with 19 and sorting)
- **Minimum:** 15
- **Maximum:** 45
- **Range:** Maximum - Minimum = 45 - 15 = 30 minutes
**(a) What happens to the range?**
The original range was 35 minutes, and the new range is 30 minutes.
- The range **decreases by 5 minutes.**
So the correct choice is:
• The range decreases by **5 minutes.**
---
**(b) What happens to the interquartile range (IQR)?**
To calculate the IQR for both the original and modified datasets, we need to find the first (Q1) and third (Q3) quartiles.
**Original Data:**
- Ordered: 10, 15, 15, 19, 25, 30, 34, 45
- Median (Q2): (19 + 25) / 2 = 22
- Q1: Median of the lower half (10, 15, 15, 19) = (15 + 15) / 2 = 15
- Q3: Median of the upper half (25, 30, 34, 45) = (30 + 34) / 2 = 32
- **IQR:** Q3 - Q1 = 32 - 15 = 17 minutes
**Modified Data:**
- Ordered: 15, 15, 19, 19, 25, 30, 34, 45
- Median (Q2): (19 + 25) / 2 = 22
- Q1: Median of the lower half (15, 15, 19, 19) = (15 + 19) / 2 = 17
- Q3: Median of the upper half (25, 30, 34, 45) = (30 + 34) / 2 = 32
- **IQR:** Q3 - Q1 = 32 - 17 = 15 minutes
So, the IQR changed from 17 minutes to 15 minutes.
**(b) What happens to the IQR?**
The IQR **decreases by 2 minutes.**
So the correct choice is:
• The IQR decreases by **2 minutes.**