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:

• Mode: The mode is the value with the highest frequency. In a density curve, this is the peak. So, the mode is at \( C \) because it is the highest point on the curve.
• Median: The median divides the area under the density curve into two equal - halves. For a right - skewed curve (assuming the tail is to the left in the given curve, if we consider the general property of skewness in terms of the position of the mean, median, and mode), the median is less than the mean. The area to the left of \( B \) and to the right of \( B \) is equal.
• Mean: The mean is affected by the tail of the distribution. In a skewed distribution, the mean is pulled in the direction of the tail. Since the tail (assuming it is a left - skewed - like situation in terms of the relative position of mean, median, mode; if we consider the general rule that for a unimodal curve, if the curve has a tail, mean is in the direction of the tail). Here, if we assume the non - peak side as a tail, the mean is at \( A \) because it is pulled towards the tail (the side with lower - density values)

Answer:

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