Brenda Had Bowling Scores Of 92, 110, 85, 78, And 96. She Completed The Steps Below To Determine The Score She Needs In Her Next Game To Have A Mean, Or Average, Bowling Score Of 96.Step 1: Find The Total Points Needed To Score In Six Games: $96

Introduction

In this article, we will explore the steps Brenda took to determine the score she needs in her next game to achieve a mean bowling score of 96. The mean, or average, is calculated by adding up all the scores and dividing by the number of games played. To find the required score for the next game, Brenda will need to calculate the total points needed to score in six games and then determine the score she needs to achieve in the next game.

Step 1: Find the Total Points Needed to Score in Six Games

To find the total points needed to score in six games, we need to multiply the desired mean score by the number of games. In this case, Brenda wants to achieve a mean score of 96 in six games.

Total points needed = Desired mean score x Number of games
Total points needed = 96 x 6
Total points needed = 576

Calculating the Current Total Points

Before we can determine the score Brenda needs in her next game, we need to calculate the current total points she has achieved in the five games she has already played. We can do this by adding up the scores of the five games.

Current total points = Score of game 1 + Score of game 2 + Score of game 3 + Score of game 4 + Score of game 5
Current total points = 92 + 110 + 85 + 78 + 96
Current total points = 461

Determining the Required Score for the Next Game

Now that we have calculated the total points needed to score in six games and the current total points, we can determine the required score for the next game. We can do this by subtracting the current total points from the total points needed.

Required score for the next game = Total points needed - Current total points
Required score for the next game = 576 - 461
Required score for the next game = 115

Conclusion

In this article, we have explored the steps Brenda took to determine the score she needs in her next game to achieve a mean bowling score of 96. We calculated the total points needed to score in six games and the current total points she has achieved in the five games she has already played. Finally, we determined the required score for the next game by subtracting the current total points from the total points needed.

Calculating the Mean Score

The mean score is calculated by adding up all the scores and dividing by the number of games played. In this case, Brenda wants to achieve a mean score of 96 in six games.

Mean score = (Score of game 1 + Score of game 2 + Score of game 3 + Score of game 4 + Score of game 5 + Required score for the next game) / Number of games
Mean score = (92 + 110 + 85 + 78 + 96 + 115) / 6
Mean score = 576 / 6
Mean score = 96

Calculating the Standard Deviation

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation = sqrt(((Score of game 1 - Mean score)^2 + (Score of game 2 - Mean score)^2 + (Score of game 3 - Mean score)^2 + (Score of game 4 - Mean score)^2 + (Score of game 5 - Mean score)^2 + (Required score for the next game - Mean score)^2) / Number of games)
Standard deviation = sqrt(((92 - 96)^2 + (110 - 96)^2 + (85 - 96)^2 + (78 - 96)^2 + (96 - 96)^2 + (115 - 96)^2) / 6)
Standard deviation = sqrt((16 + 16 + 49 + 324 + 0 + 361) / 6)
Standard deviation = sqrt(766 / 6)
Standard deviation = sqrt(127.67)
Standard deviation = 11.28

Calculating the Variance

The variance is the average of the squared differences from the mean.

Variance = ((Score of game 1 - Mean score)^2 + (Score of game 2 - Mean score)^2 + (Score of game 3 - Mean score)^2 + (Score of game 4 - Mean score)^2 + (Score of game 5 - Mean score)^2 + (Required score for the next game - Mean score)^2) / Number of games
Variance = (16 + 16 + 49 + 324 + 0 + 361) / 6
Variance = 766 / 6
Variance = 127.67

Calculating the Coefficient of Variation

The coefficient of variation is a measure of relative variability.

Coefficient of variation = Standard deviation / Mean score
Coefficient of variation = 11.28 / 96
Coefficient of variation = 0.117

Conclusion

Q: What is the desired mean score that Brenda wants to achieve in six games?

A: The desired mean score that Brenda wants to achieve in six games is 96.

Q: How do you calculate the total points needed to score in six games?

A: To calculate the total points needed to score in six games, you multiply the desired mean score by the number of games.

Total points needed = Desired mean score x Number of games
Total points needed = 96 x 6
Total points needed = 576

Q: What is the current total points that Brenda has achieved in the five games she has already played?

A: The current total points that Brenda has achieved in the five games she has already played is 461.

Current total points = Score of game 1 + Score of game 2 + Score of game 3 + Score of game 4 + Score of game 5
Current total points = 92 + 110 + 85 + 78 + 96
Current total points = 461

Q: How do you determine the required score for the next game?

A: To determine the required score for the next game, you subtract the current total points from the total points needed.

Required score for the next game = Total points needed - Current total points
Required score for the next game = 576 - 461
Required score for the next game = 115

Q: What is the mean score that Brenda will achieve in six games if she scores 115 in the next game?

A: The mean score that Brenda will achieve in six games if she scores 115 in the next game is 96.

Mean score = (Score of game 1 + Score of game 2 + Score of game 3 + Score of game 4 + Score of game 5 + Required score for the next game) / Number of games
Mean score = (92 + 110 + 85 + 78 + 96 + 115) / 6
Mean score = 576 / 6
Mean score = 96

Q: What is the standard deviation of Brenda's scores in the six games?

A: The standard deviation of Brenda's scores in the six games is 11.28.

Standard deviation = sqrt(((Score of game 1 - Mean score)^2 + (Score of game 2 - Mean score)^2 + (Score of game 3 - Mean score)^2 + (Score of game 4 - Mean score)^2 + (Score of game 5 - Mean score)^2 + (Required score for the next game - Mean score)^2) / Number of games)
Standard deviation = sqrt(((92 - 96)^2 + (110 - 96)^2 + (85 - 96)^2 + (78 - 96)^2 + (96 - 96)^2 + (115 - 96)^2) / 6)
Standard deviation = sqrt((16 + 16 + 49 + 324 + 0 + 361) / 6)
Standard deviation = sqrt(766 / 6)
Standard deviation = sqrt(127.67)
Standard deviation = 11.28

Q: What is the variance of Brenda's scores in the six games?

A: The variance of Brenda's scores in the six games is 127.67.

Variance = ((Score of game 1 - Mean score)^2 + (Score of game 2 - Mean score)^2 + (Score of game 3 - Mean score)^2 + (Score of game 4 - Mean score)^2 + (Score of game 5 - Mean score)^2 + (Required score for the next game - Mean score)^2) / Number of games
Variance = (16 + 16 + 49 + 324 + 0 + 361) / 6
Variance = 766 / 6
Variance = 127.67

Q: What is the coefficient of variation of Brenda's scores in the six games?

A: The coefficient of variation of Brenda's scores in the six games is 0.117.

Coefficient of variation = Standard deviation / Mean score
Coefficient of variation = 11.28 / 96
Coefficient of variation = 0.117

Conclusion

In this Q&A article, we have answered some common questions related to calculating the required bowling score for a desired mean. We have covered topics such as calculating the total points needed to score in six games, determining the required score for the next game, and calculating the mean score, standard deviation, variance, and coefficient of variation.