To analyze the two distributions from your image and determine the greatest measure of center and variability, I’ll walk through the steps:

1. Measure of Center:

The measure of center is typically represented by the mean, median, or mode. Visually:

• Distribution 1a: The data appears to be centered around values like -12 and -5, though it is somewhat bimodal with peaks near these two points.
• Distribution 1b: The data is more concentrated, and the center seems to be around -10.

Conclusion on Center: Distribution 1b has the greatest measure of center, as its values cluster around -10, while Distribution 1a is more spread out and appears bimodal.

2. Measure of Variability:

The measure of variability indicates the spread of the data and can be measured by range, variance, or standard deviation.

• Distribution 1a: The values are spread across a wider range, from -16 to -3, with notable gaps between clusters of data.
• Distribution 1b: The values are more concentrated and fall between -16 and -6, indicating a smaller spread compared to 1a.

Conclusion on Variability: Distribution 1a has the greatest variability, as it has more widely spaced clusters and covers a broader range of values.

Summary:

• Greatest measure of center: Distribution 1b (center around -10).
• Greatest measure of variability: Distribution 1a (wider spread).

Do you want any further details on these calculations or explanations?

Here are five related questions:

1. How would you calculate the exact mean for each distribution?
2. What is the role of the standard deviation in describing variability?
3. How would identifying the mode help in these distributions?
4. Could these distributions be considered normal? Why or why not?
5. What effect would outliers have on the measure of center in each case?

Tip: Variability is important in understanding the reliability of the measure of center. Higher variability means the data is more spread out, which could reduce the reliability of the mean.