Question

1. a density curve that models the distribution of a quantitative variable is shown here: identify the location of the mean, median, and mode by letter. justify your answers.

Explanation:

Step1: Identify the mode

The mode is the value with the highest frequency. In a density curve, it is the peak. So, the mode is at \( A \).

Step2: Analyze the median

The median divides the area under the curve into two equal - halves. For a right - skewed curve (tail on the right), the median is less than the mean. Since the curve is right - skewed (assuming the general shape from the problem description, as the peak is on the left and there is a tail on the right), and we know that the median is the "balance point" for area.

Step3: Analyze the mean

The mean is affected by the tail. In a right - skewed distribution, the mean is pulled towards the tail. So, the mean is at \( C \) and the median is at \( B \)

Answer:

Mode: \( A \) (highest point of the curve). Median: \( B \) (divides the area under the curve into two equal parts). Mean: \( C \) (pulled towards the right - hand tail of the skewed distribution)