Question

The dot plot below shows the drawing scores of some students:

A number line is shown from 1 to 5 in increments of 1. The horizontal axis label is Score. There are 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, and 1 dot above 5. The title of the line plot is Dance Scores.

Which statement best describes the shape of the data?

It is symmetric and has a peak at 1.
It is symmetric and has a peak at 5.
It is not symmetric and has a peak at 1.
It is not symmetric and has a peak at 5.

Answer 1

Answer: THE ANSWER IS B

Explanation:

Let's think of this problem easily by looking at it instead of going through rigorous mathematics.

When a graph is skewed right, most of the values are to the left side.

When a graph is skewed left, most of the values are to the right side.

Perfectly symmetrical is that both sides, with respect to the median, are same. Here mean and median is equal.

Nearly symmetrical would really close to perfect symmetry, only varying a bit on both sides. Mean would be approximately equal to median.

Now counting the dots as well as looking closely, we can rule out skewed right and skewed left. Now, is the graph perfectly symmetrical? No! So the correct answer is "nearly symmetrical". Correct choice is B.

ANSWER: B

Answer 2

It is not symmetric and has a peak at 1

Explanation:

It is easier to see with a graph, but from the information given, you can see a linear trend downwards. From my knowledge, the definition of symmetric means it would look the same if flipped, which it would not. It is in a linear direction downwards from 1 to 5, decreasing by 1 in every category. This means that it is not symmetric and its peak is at 1.