this table shows larry's bowling scores. which best describes the result if Larry bowls 150 in his 5th game?

game bowling score
1 128
2 142
3 136
4 142

the median stays the same
the range increases by 8
the mean increases by 2
the mode increases by 8

1 answer

To analyze the impact of Larry's 5th game score of 150 on his bowling scores, let's first determine the current statistics: the median, range, mean, and mode of the first four games.

Current Scores:

  • Game 1: 128
  • Game 2: 142
  • Game 3: 136
  • Game 4: 142

Step 1: Calculate the Median

To find the median, we need to sort the scores:

  • 128, 136, 142, 142

The median is the average of the two middle numbers (136 and 142):

  • Median = (136 + 142) / 2 = 139

Step 2: Calculate the Range

The range is determined by subtracting the lowest score from the highest score:

  • Lowest score = 128
  • Highest score = 142
  • Range = 142 - 128 = 14

Step 3: Calculate the Mean

Mean is the average of the scores:

  • Mean = (128 + 142 + 136 + 142) / 4 = 548 / 4 = 137

Step 4: Calculate the Mode

The mode is the score that occurs most frequently:

  • In this case, the mode is 142 (occurs twice).

Step 5: Include the 5th Game Score of 150

Now let's update the statistics with the new score of 150.

New Scores:

  • 128, 136, 142, 142, 150

New Median

  • Sorted: 128, 136, 142, 142, 150
  • Median = 142 (the middle score).

New Range

  • New highest score = 150
  • New range = 150 - 128 = 22

New Mean

  • Mean = (128 + 136 + 142 + 142 + 150) / 5 = 698 / 5 = 139.6 (this means it increases, but we'll check how much).

New Mode

The mode remains the same because 142 still occurs twice while all other scores occur only once.

Summary of Changes:

  • Median updated from 139 to 142 (increased).
  • Range increased from 14 to 22 (increased by 8).
  • Mean increased from 137 to 139.6 (increased by 2.6, approximately).
  • Mode remains at 142 (not increased).

Conclusion:

The correct statement is that the range increases by 8.