Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Jack has the following scores on exams in his math class.
81, 87, 93, 89, 61, 81
If he wants to make his performance sound as good as possible, which measure should he use—the mean, the median, or the mode of his exam grades when he talks about how he is doing? Explain.
In you response, make sure to:
calculate the mean,
calculate the median, and
calculate the mode of his exam grades
compare and pick the measure that makes his performance sound as good as possible.
https://www.purplemath.com/modules/meanmode.htm
Read carefully and follow directions. Let the math tutors know what you come up with so someone can check your answers.
To determine which measure Jack should use to make his performance sound as good as possible, we need to calculate the mean, median, and mode of his exam grades.
Here are the steps to calculate each measure:
1. Mean: The mean is calculated by summing up all the scores and dividing by the total number of scores.
The scores given are: 81, 87, 93, 89, 61, 81
Add up the scores: 81 + 87 + 93 + 89 + 61 + 81 = 492
Divide by the total number of scores: 492 / 6 = 82
Therefore, the mean score is 82.
2. 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.
Arrange the scores in ascending order: 61, 81, 81, 87, 89, 93
Since there are 6 scores, the middle two scores are 81 and 87.
Take the average of the two middle scores: (81 + 87) / 2 = 84
Therefore, the median score is 84.
3. Mode: The mode is the score(s) that appear most frequently. If no score repeats, there is no mode.
In this case, the most frequent score is 81 since it appears twice.
Therefore, the mode score is 81.
Now, let's compare the mean, median, and mode:
- Mean: The mean score is 82.
- Median: The median score is 84.
- Mode: The mode score is 81.
To make his performance sound as good as possible, Jack should use the measure that reflects his performance as high as possible. Since the mean is the lowest among the three measures, Jack should avoid using the mean score when talking about his performance. Instead, he can mention either the median score of 84 or the mode score of 81 to make his performance sound better.