Question

calculus grades (1.6) the dotplot shows final exam scores for mr. miller’s 25 calculus students. a. find the median exam score.b. Without doing any calculations, would you estimate that the mean is about the same as the median, higher than the median, or lower than the median?

Answer 1

The median exam score is 1.6.

Step-by-step explanation:

To find the median exam score, we need to first arrange the scores in ascending order. Looking at the dotplot, we can see that the middle value is 1.6. Since there are 25 students, the median will be the average of the 12th and 13th scores, which are both 1.6. So, the median exam score is 1.6.

In this case, it is difficult to estimate whether the mean is about the same as the median, higher than the median, or lower than the median without doing any calculations. The dotplot does not provide enough information about the distribution of the exam scores. We would need to know more about the individual scores to estimate the mean in relation to the median.

Answer 2

a. The median is 89. b. The data distribution is left-skewed, hence, the mean will likely be less than the median because the mean is affected by the low values in the long tail.

What is the median?

The median is the middle value of a data set that is ordered, and it can simply be identified on a dot plot by looking for the data value where the center value falls on.

a. In the diagram showing the dot plot referred to, the median would be the 13th value since there are 25 students. Thus, the 13th value falls on 89.

b. The data in the dot plot is skewed left (left skewed), therefore, the mean will likely be less than the median because the mean is affected by the low values in the long tail in the given distribution that is skewed to the left.