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.
please help connexus academy please
To determine which measure Jack should use to make his performance sound as good as possible, let's calculate the three measures: the mean, the median, and the mode of his exam grades.
1. Mean:
The mean is calculated by adding up all the values and dividing the sum by the number of values. For Jack's exam scores, we have:
81 + 87 + 93 + 89 + 61 + 81 = 492
To get the mean, we divide the sum by the number of values, which is 6:
Mean = 492 / 6 ≈ 82
2. Median:
The median is the middle value when the exam scores are arranged in numerical order. In this case, Jack's exam scores arranged in order are:
61, 81, 81, 87, 89, 93
Since there are an even number of scores, we take the average of the two middle values, which are 81 and 87.
Median = (81 + 87) / 2 = 84
3. Mode:
The mode is the most frequently occurring value. In this case, there are two values that occur twice, which are 81 and 93. Therefore, the mode of Jack's exam scores is both 81 and 93.
Now let's compare the mean, median, and mode as measures of Jack's performance. If Jack wants to make his performance sound as good as possible, he should choose the measure that presents his scores in the most positive light.
In this case, the mean of his exam grades is 82, which represents an overall average score. The median is 84, which suggests a slightly higher score than the mean. The mode, however, includes 81 and 93, which are the highest and lowest scores in the data set. This might give the impression of a wider range of scores and potentially a more challenging class.
Therefore, if Jack wants to make his performance sound as good as possible, he should use the median of his exam grades when discussing his performance.
mean: add 'em up and divide by 6
median: sort low to high. Since there is an even number of grades, the median is the average of the middle two.
mode: the grade that occurs most often