Sally's scores on her science quizzes are listed below. Which average best represents Sally's scores? Explain reasoning.
SCORES: 86 78 70 68 95 81 85 89 95
Sally receives a score of 100 on the next quiz. How does this score affect the mean, median and modes of Sally's Scores?
Please read the easy info at the following site:
http://math.about.com/library/weekly/aa020502a.htm
If you still don't get it, we can help you more.
To find the average that best represents Sally's scores, we need to calculate the mean, median, and modes of her scores.
First, let's calculate the mean. The mean is found by summing up all the scores and dividing by the number of scores. In this case, Sally's scores are:
86, 78, 70, 68, 95, 81, 85, 89, 95
To find the mean, we add up all the scores:
86 + 78 + 70 + 68 + 95 + 81 + 85 + 89 + 95 = 737
And divide by the number of scores, which is 9:
737 / 9 = 81.89
So, the mean of Sally's scores is approximately 81.89.
Next, let's find the median. The median is the middle value when the scores are arranged in ascending order. If there is an even number of scores, the median is the average of the two middle values.
Arranging Sally's scores in ascending order:
68, 70, 78, 81, 85, 86, 89, 95, 95
There are 9 scores, so the middle value is the 5th score, which is 85.
Therefore, the median of Sally's scores is 85.
Finally, let's find the modes. The mode is the value(s) that appear most frequently in the set of scores.
In Sally's scores, the numbers 95 appear twice, which is more frequently than any other score. So, the mode of Sally's scores is 95.
Now let's consider how Sally's score of 100 on the next quiz will affect the mean, median, and modes of her scores.
If Sally receives a score of 100 on the next quiz, we need to recalculate the mean, median, and modes considering this new score.
If we add the score of 100 to Sally's scores:
86, 78, 70, 68, 95, 81, 85, 89, 95, 100
The new mean can be found by summing up all the scores and dividing by the number of scores:
737 + 100 = 837
And dividing by the new number of scores, which is 10:
837 / 10 = 83.7
So, the new mean of Sally's scores is approximately 83.7.
The new median can be found by rearranging the scores in ascending order:
68, 70, 78, 81, 85, 86, 89, 95, 95, 100
There are now 10 scores. The middle value(s) will be the 5th and 6th score, which are 85 and 86.
Therefore, the new median of Sally's scores is the average of 85 and 86:
(85 + 86) / 2 = 85.5
The new modes can be found by checking which score(s) appear most frequently in the new set. In this case, the mode(s) will remain the same as before, as the score of 100 does not change the frequencies of the other scores.
So, the modes of Sally's scores remain as 95.
In summary, Sally's score of 100 on the next quiz will increase the mean to approximately 83.7, slightly increase the median to 85.5, and not change the modes, which remain as 95.