The mean of the scores of three
students in a class is 9. If the modal
score is 11, find the lowest score.
that would be 5
pls steve! Help me, i need the solution on how to solve this type of question.
please Steve help me. I need the steps on how to get the answer
This one is really quite simple, if you understand what the mean and mode are.
The mode is the most frequent score. Since there are only three scores, and the mode is 11, it must occur more than any other score. That is, 11 occurs twice.
Since the mean is 9, the sum of the three scores is 3*9 = 27.
Since two of the scores are 11, the third score must be 5, since
11+11+5 = 27
thank you sir!
To find the lowest score, we need to know the mode of the scores and the mean of the scores.
Given that the mean of the scores is 9, it means that if we add up all three scores and divide by 3, we will get 9.
So, let's denote the three scores as x, y, and z. We have the equation:
(x + y + z) / 3 = 9
Multiplying both sides by 3 to get rid of the denominator, we have:
x + y + z = 27
Next, we know that the mode of the scores is 11. The mode is the value that appears most frequently in the data set. In this case, one of the scores occurred more often than the others, and that score is 11.
Let's consider two scenarios to find the lowest score:
Scenario 1: The lowest score is 11
If the lowest score is 11, then two of the scores must also be 11 because the mode is 11. In that case, we have:
11 + 11 + z = 27
22 + z = 27
z = 27 - 22
z = 5
So, if the lowest score is 11, then the other two scores are also 11 and 5.
Scenario 2: The lowest score is not 11
If the lowest score is not 11, then all three scores must be different. In that case, we have:
x + y + z = 27
Since the mean is 9, and we are looking for the lowest score, let's assume x is the lowest score. So, x = 9. Subtracting x from both sides, we have:
y + z = 18
Since we also know that the mode is 11, either y or z must be 11. Let's assume y is 11:
11 + z = 18
z = 18 - 11
z = 7
So, if the lowest score is not 11, then the scores are 9, 11, and 7.
Comparing the two scenarios, we see that the lowest score is 5.
Therefore, the lowest score is 5.