Question

the dot plot shows the data gavin collects to answer the question what is a typical number of seconds that i can stay in a handstand?
a. why is gavins question a statistical question?
b. describe the shape and variability of the distribution of gavins data set.

Explanation:

Part a

A statistical question is one that anticipates a variety of answers. Gavin's question "What is a typical number of seconds that I can stay in a handstand?" implies that there will be multiple data points (different handstand times) collected. Since the data (as shown in the dot - plot) will have variability (different times), it is a statistical question.

Part b

• Shape:
• Symmetry/Asymmetry: The distribution is not symmetric. If we consider the number of dots on either side of a central value, there is no mirror - like image.
• Peak: The peak (mode) is at \(3\) seconds as there are more dots (representing data points) at \(3\) than at other values.
• Variability:
• The data ranges from \(1\) second to \(6\) seconds. We can also look at the spread. The values are not all clustered closely together. For example, there is a single data point at \(6\) which is relatively far from the main cluster (around \(1 - 4\) seconds).

Answer:

a. Gavin's question is a statistical question because it expects a set of data (handstand times) with variability (different times will be recorded).
b.

• Shape: The distribution has a peak (mode) at \(3\) seconds and is not symmetric.
• Variability: The data ranges from \(1\) to \(6\) seconds, indicating some spread in the handstand times.