the mean score on a math test taken by 15 students was 82%. one more student takes the test late and earns 93%. what is the new mean score? please show work
15 * 82 = 1230
1230 + 93 = 1323
1323 / 15 = 82.69
The sum of the original 15 students must have been
15(82) or 1230
So now we add on 93 to get a new total of 1323
but to get the new average, we must now divide this by 16
1323/16 = 82.6875 or 83% to the nearest whole number.
so the average doesnt change?
Yes the average changed -- from 82 to 82.6875 -- rounded to 83%
To find the new mean score, we need to calculate the sum of all the scores and divide it by the total number of students.
Step 1: Calculate the sum of all the scores.
The mean score of 15 students was 82%. So, the sum of their scores can be calculated by multiplying the mean by the total number of students.
Sum_of_scores = Mean_score * Number_of_students
Sum_of_scores = 82% * 15
To calculate 82% of 15, multiply 82% by 0.01 and then multiply the result by 15.
Sum_of_scores = 0.82 * 15
Step 2: Add the additional score to the sum of scores.
One more student takes the test late and earns 93%. We need to add this score to the sum of scores calculated in the previous step.
New_Sum_of_scores = Sum_of_scores + Additional_score
New_Sum_of_scores = 0.82 * 15 + 93%
To calculate 93% of 1, multiply 93% by 0.01 and then multiply the result by 1.
New_Sum_of_scores = 0.82 * 15 + 0.93 * 1
Step 3: Calculate the new mean score.
To find the new mean score, divide the new sum of scores by the total number of students, including the additional student.
New_Mean_score = New_Sum_of_scores / (Number_of_students + 1)
New_Mean_score = (0.82 * 15 + 0.93 * 1) / (15 + 1)
Calculating this expression will give us the desired new mean score. Let's calculate it.
New_Mean_score = (12.3 + 0.93) / 16
New_Mean_score = 13.23 / 16
New_Mean_score ≈ 0.8269
Therefore, the new mean score is approximately 0.8269, which is equivalent to 82.69%.