To find the Interquartile Range (IQR) of the given data set, we first need to organize the data in ascending order and then determine the first quartile (Q1) and the third quartile (Q3).
Step 1: Sort the Data
The sorted data set is:
- 287, 287, 290, 295, 329, 365, 387, 389, 397
Step 2: Find Q1 and Q3
Q1 (the first quartile) is the median of the lower half of the data (the lower 50%):
- The lower half: 287, 287, 290, 295 (the median is the average of the two middle numbers)
- Q1 = (287 + 290) / 2 = 288.5
Q3 (the third quartile) is the median of the upper half of the data (the upper 50%):
- The upper half: 329, 365, 387, 389, 397 (the median is the average of the two middle numbers)
- Q3 = (387 + 389) / 2 = 388
Step 3: Calculate the IQR
IQR = Q3 - Q1 = 388 - 288.5 = 99.5
Interpretation of the IQR
The IQR of 99.5 indicates the range within which the central 50% of the data points lie. A larger IQR suggests more variability in the middle 50% of the data. In this context, it can suggest that there is a considerable spread in the values of the player's scores, indicating varying performance.
Overall, the IQR is a measure of the spread of the data that helps to identify potential outliers and assess the consistency of player performance. In this case, the variability in the player's scores may suggest fluctuating performance in the game.