Question
A video game player had the following stores 287 389 287 329 295 290 397 387-365 what does the IQR indicate about the data set
Answers
GPT-4o mini
To analyze the dataset provided (287, 389, 287, 329, 295, 290, 397, 387, 365) and determine the Interquartile Range (IQR), follow these steps:
1. **Sort the Data**: First, sort the data in ascending order:
```
287, 287, 290, 295, 329, 365, 387, 389, 397
```
2. **Find the Quartiles**:
- **Median (Q2)**: The median is the middle value of the sorted data. For a dataset of 9 values, the median is the 5th value:
- Median \(Q2\) = 329
- **Lower Quartile (Q1)**: Q1 is the median of the first half of the data (first four values):
```
287, 287, 290, 295
```
The median of this subset is the average of the second and third values:
- Q1 = (287 + 290) / 2 = 288.5
- **Upper Quartile (Q3)**: Q3 is the median of the second half of the data (last four values):
```
365, 387, 389, 397
```
The median of this subset is the average of the second and third values:
- Q3 = (387 + 389) / 2 = 388
3. **Calculate the IQR**:
\[
\text{IQR} = Q3 - Q1 = 388 - 288.5 = 99.5
\]
### Conclusion:
The IQR is **99.5**.
The IQR helps to determine the spread or variability of the middle 50% of the dataset. A larger IQR indicates a wider spread, while a smaller IQR suggests that the data points are closer together. In this case, an IQR of 99.5 suggests that there is a significant spread in the scores around the median, indicating variability in the player's performance or game stores.
1. **Sort the Data**: First, sort the data in ascending order:
```
287, 287, 290, 295, 329, 365, 387, 389, 397
```
2. **Find the Quartiles**:
- **Median (Q2)**: The median is the middle value of the sorted data. For a dataset of 9 values, the median is the 5th value:
- Median \(Q2\) = 329
- **Lower Quartile (Q1)**: Q1 is the median of the first half of the data (first four values):
```
287, 287, 290, 295
```
The median of this subset is the average of the second and third values:
- Q1 = (287 + 290) / 2 = 288.5
- **Upper Quartile (Q3)**: Q3 is the median of the second half of the data (last four values):
```
365, 387, 389, 397
```
The median of this subset is the average of the second and third values:
- Q3 = (387 + 389) / 2 = 388
3. **Calculate the IQR**:
\[
\text{IQR} = Q3 - Q1 = 388 - 288.5 = 99.5
\]
### Conclusion:
The IQR is **99.5**.
The IQR helps to determine the spread or variability of the middle 50% of the dataset. A larger IQR indicates a wider spread, while a smaller IQR suggests that the data points are closer together. In this case, an IQR of 99.5 suggests that there is a significant spread in the scores around the median, indicating variability in the player's performance or game stores.