Question

choose the best answer to the following question. explain your reasoning
one hundred students take a chemistry exam. all but two of the students score between 55 and 76 points, but one student gets a 31 and one student gets a 96. what do the scores 31 and 96 represent?
choose the correct answer below
a. they represent mean scores. they are computed by adding the exam scores and then dividing by the number of exams
b. they represent outliers. one is much lower than most of the values, and one is much higher than most of the values
c. they represent skewed scores. the two scores increase the variation of the distribution
d. they represent outliers. these values will change the mean, median, and mode of the data set
e. they represent skewed scores. one causes the distribution to spread to the left, and one causes the distribution to spread to the right
f. they represent mean scores. they are the lower and higher averages, respectively

Explanation:

An outlier is a data point that is significantly different from other data points in a dataset. In this case, 31 is much lower than the majority of scores (which are between 55 - 76) and 96 is much higher. Mean scores are calculated by the formula $\frac{\sum_{i = 1}^{n}x_{i}}{n}$ (where $x_{i}$ are data points and $n$ is the number of data points), and these two scores are not means. Skewed scores relate to the shape of the distribution (left - skewed or right - skewed), but the key characteristic here is being extreme values (outliers). Also, outliers do not necessarily change the mode (the most frequently occurring value), and while they can affect the mean and median, the core identification is based on being extreme relative to most data.

Answer:

B. They represent outliers. One is much lower than most of the values, and one is much higher than most of the values.