Question

Which one of the following is a false statement about density curves?

1) Density curves are always symmetric.
2) Density curves are always bell-shaped.
3) Density curves can have multiple modes.
4) Density curves can have negative values.

Answer 1

The false statements about density curves are that they are always symmetric or always bell-shaped, and that they can have negative values. Density curves can be asymmetrical and have multiple modes, and they must be on or above the horizontal axis.

Step-by-step explanation:

The false statement about density curves is that "Density curves are always symmetric." Density curves can display a variety of shapes and are not restricted to being symmetric. While some density curves, such as those for normal distributions, are symmetric, others can be skewed to the left or right (asymmetrical). Furthermore, density curves can have multiple modes, which means they can have more than one peak. However, it is also incorrect to say that density curves are always bell-shaped or that density curves can have negative values; by definition, density curves must be on or above the horizontal axis as they represent probabilities.