Question
The prices (in dollars) of a variety of gaming consoles are shown below in order from least to greatest.
150, 300, 340, 349, 379, 399, 400, 450, 500
Suppose that the price of 349 dollars changes to 320 dollars. Answer the following.
What happens to the range?
* A. The range (choose one. increases, decreases) by ___ points.
* B. The range stays the same.
*
* What happens to the interquartile range (IQR)?
* A. The IQR (choose one. increases, decreases) by ___ points.
* B. The IQR stays the same.
150, 300, 340, 349, 379, 399, 400, 450, 500
Suppose that the price of 349 dollars changes to 320 dollars. Answer the following.
What happens to the range?
* A. The range (choose one. increases, decreases) by ___ points.
* B. The range stays the same.
*
* What happens to the interquartile range (IQR)?
* A. The IQR (choose one. increases, decreases) by ___ points.
* B. The IQR stays the same.
Answers
GPT-4o mini
To find the range and interquartile range (IQR), let's first analyze the initial data set and then the data set after the change.
**Initial Data Set:**
Prices: 150, 300, 340, 349, 379, 399, 400, 450, 500
- **Range**: The range is calculated as the difference between the maximum and minimum values.
- Range = Max - Min = 500 - 150 = 350
**Modified Data Set** (with the price changing from 349 to 320):
Prices: 150, 300, 320, 340, 379, 399, 400, 450, 500
- **Range**: After the change, the new range is:
- Range = 500 - 150 = 350 (The maximum and minimum values have not changed)
So for the range:
* A. The range **stays the same**.
* B. The range does **not** change (by 0 points).
---
Next, we calculate the interquartile range (IQR).
**Finding the IQR for the Initial Data Set:**
1. The median (Q2) is the average of the 4th and 5th values:
- Q2 = (349 + 379) / 2 = 364
2. Q1 (the median of the first half) is the average of the 2nd and 3rd values:
- Q1 = (300 + 340) / 2 = 320
3. Q3 (the median of the second half) is the average of the 6th and 7th values:
- Q3 = (399 + 400) / 2 = 399.5
**IQR for Initial Data Set:**
- IQR = Q3 - Q1 = 399.5 - 320 = 79.5
**Finding the IQR for the Modified Data Set:**
1. Q1 is still (300 + 320) / 2 = 310 since 320 replaces 349 which was higher.
2. Q3 remains the same because now we are looking at the second half:
- Q3 will still be (399 + 400) / 2 = 399.5
**IQR for Modified Data Set:**
- IQR = Q3 - Q1 = 399.5 - 310 = 89.5
Now we can see how the IQR changed:
* A. The IQR **increases** by (89.5 - 79.5) = 10 points.
* B. The IQR does **not** stay the same.
**Final Answers:**
* For the range: A. stays the same (0 points).
* For the IQR: A. increases by 10 points.
**Initial Data Set:**
Prices: 150, 300, 340, 349, 379, 399, 400, 450, 500
- **Range**: The range is calculated as the difference between the maximum and minimum values.
- Range = Max - Min = 500 - 150 = 350
**Modified Data Set** (with the price changing from 349 to 320):
Prices: 150, 300, 320, 340, 379, 399, 400, 450, 500
- **Range**: After the change, the new range is:
- Range = 500 - 150 = 350 (The maximum and minimum values have not changed)
So for the range:
* A. The range **stays the same**.
* B. The range does **not** change (by 0 points).
---
Next, we calculate the interquartile range (IQR).
**Finding the IQR for the Initial Data Set:**
1. The median (Q2) is the average of the 4th and 5th values:
- Q2 = (349 + 379) / 2 = 364
2. Q1 (the median of the first half) is the average of the 2nd and 3rd values:
- Q1 = (300 + 340) / 2 = 320
3. Q3 (the median of the second half) is the average of the 6th and 7th values:
- Q3 = (399 + 400) / 2 = 399.5
**IQR for Initial Data Set:**
- IQR = Q3 - Q1 = 399.5 - 320 = 79.5
**Finding the IQR for the Modified Data Set:**
1. Q1 is still (300 + 320) / 2 = 310 since 320 replaces 349 which was higher.
2. Q3 remains the same because now we are looking at the second half:
- Q3 will still be (399 + 400) / 2 = 399.5
**IQR for Modified Data Set:**
- IQR = Q3 - Q1 = 399.5 - 310 = 89.5
Now we can see how the IQR changed:
* A. The IQR **increases** by (89.5 - 79.5) = 10 points.
* B. The IQR does **not** stay the same.
**Final Answers:**
* For the range: A. stays the same (0 points).
* For the IQR: A. increases by 10 points.