a teacher made a line plot to score of a quiz . after 2 more students took quiz the mean score was 16 plot 2 possible scores on the line plot to make the mean 16
Idk
Yes please find an explanation.
Thank you
To solve this problem, we need to first determine the scores of the existing students and then plot two possible scores that could be added to the line plot to make the mean score 16.
Let's say the teacher initially had 8 students who took the quiz and their scores were as follows:
10, 12, 14, 16, 18, 20, 22, 24
The mean score of these 8 students is calculated by adding up all the scores and dividing by the number of students:
Mean = (10 + 12 + 14 + 16 + 18 + 20 + 22 + 24) / 8 = 136 / 8 = 17
However, after 2 more students took the quiz, the mean score became 16. Thus, the total scores of all 10 students must be:
Mean x Number of students = 16 x 10 = 160
Now, we need to find two numbers that can be added to the existing scores to make the total sum equal to 160. These numbers should also be feasible scores for the quiz.
Let's assume the two additional scores are x and y. The equation can be set up as follows:
(10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + x + y) / 10 = 16
By rearranging the equation, we can solve for x + y:
10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + x + y = 160
x + y = 160 - (10 + 12 + 14 + 16 + 18 + 20 + 22 + 24)
x + y = 160 - 136
x + y = 24
Now, we can select two possible scores that satisfy the equation and make the mean 16. Here is one possible solution:
x = 10
y = 14
By adding these scores to the line plot, the mean score would become 16.
Please note that there are multiple possible solutions, and other valid combinations of x and y could also be used to achieve the mean of 16.
To plot two possible scores on the line plot to make the mean score 16, you will need to follow these steps:
Step 1: Understand the given information
The teacher made a line plot of the scores of a quiz. After two more students took the quiz, the mean score is 16. This means that the current line plot does not include the two additional scores.
Step 2: Determine the current mean score
Take a look at the existing line plot and calculate the mean score based on the available data. The mean score is the sum of all the scores divided by the total number of scores.
Step 3: Calculate the sum of the existing scores
Add up all the scores represented on the line plot.
Step 4: Determine the current number of scores
Count the number of scores on the line plot.
Step 5: Calculate the current mean score
Divide the sum of the existing scores by the current number of scores.
Step 6: Identify the gap between the current mean and the desired mean
Subtract the current mean score from the desired mean score (16 in this case). The result will give you the difference between the desired mean and the current mean.
Step 7: Determine the number of scores needed
Since you have two additional students who took the quiz, you will need to figure out how much each of their scores can contribute to closing the gap between the current mean and the desired mean. Divide the difference obtained in Step 6 by 2 (the number of additional students).
Step 8: Plot the scores
To make the mean score 16, you will need to plot two scores on the line plot that will close the gap between the current mean and the desired mean. Add the score calculated in Step 7 to the existing line plot twice, ensuring that the new scores are evenly spaced apart.
By following these steps, you should be able to plot two possible scores on the line plot to make the mean score 16.