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

Question

The IQR of 329 indicates that the center of the data is around the score the IQR of 99.5 indicates that average order was not the IQR of 99.5 indicates with the video game player had a relatively small variability for their middle scores

Answer 1

To calculate the interquartile range (IQR) of the given data set, we need to first order the data from least to greatest and then find the first quartile (Q1) and the third quartile (Q3). The IQR is calculated as IQR = Q3 - Q1.

1. Ordered Data Set:

   • Original scores: 287, 389, 287, 329, 295, 290, 397, 387, 365
   • Ordered scores: 287, 287, 290, 295, 329, 365, 387, 389, 397

2. Finding Q1 and Q3:

   • Q1 (the median of the first half) is the median of 287, 287, 290, 295. This gives us (287 + 290) / 2 = 288.5.
   • The scores in the first half are 287, 287, 290, 295 (4 values).
   • Q3 (the median of the second half) is the median of 365, 387, 389, 397. This gives us (389 + 365) / 2 = 377.
   • The scores in the second half are 365, 387, 389, 397 (4 values).

3. Calculating IQR:

   • IQR = Q3 - Q1 = 377 - 288.5 = 88.5.

Interpretation:

• IQR of 88.5: This indicates the range within which the middle 50% of the scores lie. A smaller IQR generally indicates that there is less variability among the central scores of the dataset.

• Variability: If the IQR is relatively small, it suggests that the player has consistent scoring among their middle scores.

Summary of Your Statements:

• The IQR of the dataset reflects that the central scores (Q1 to Q3) have relatively low variability, indicating that the video game player's scoring was fairly consistent. The statement that "the IQR of 99.5 indicates that average order was not" seems to be erroneous. The calculated IQR is 88.5, not 99.5, and it suggests a relatively small variability for the player's middle scores.