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

Answer 1

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.