A video game player had the following scores: 287, 389, 287, 329, 295, 290, 397, 387, 365. What does the IQR indicate about this dataset?
The interquartile range (IQR) indicates the spread or variability of the middle 50% of the data. To calculate the IQR, we first need to arrange the data in ascending order:
287, 287, 290, 295, 329, 365, 387, 389, 397
Now, we find the median of the entire dataset, which is the number that falls in the middle when the data is arranged in order. In this case, the median is 329.
Next, we find the median of the lower half of the data (Q1) and the median of the upper half of the data (Q3). Q1 is the median of the numbers below 329, and Q3 is the median of the numbers above 329. In this case:
Q1 = (290 + 295)/2 = 292.5
Q3 = (387 + 389)/2 = 388
Now, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 388 - 292.5 = 95.5
Therefore, the IQR of this dataset is 95.5. This indicates that the middle 50% of the scores have a spread of 95.5 points.