If two distributions of scores have the same mean, the distribution in which scores are more tightly clustered around the mean will have a larger standard deviation than the distribution in which scores are more spread out.

Suppose a researcher compares two distributions of test scores that both have an identical mean of 10. The first distribution has a standard deviation of 1.69, while the second distribution has a standard deviation of 4.30. Based on the concept of standard deviation, what does the value of 4.30 indicate about the second distribution?

Examine the provided image showing two distributions of psychology test scores, both with a mean of 10. Arrange the following steps in the logical sequence required to analyze why the red distribution has a standard deviation of 4.30 while the blue distribution has a standard deviation of 1.69.

In the provided example of two distributions with a mean of $10$, what does a standard deviation of $1.69$ specifically represent?

If a distribution of psychology quiz scores has a mean of $10$ and a standard deviation of $1.69$, it means that every individual score in the distribution must lie within $1.69$ units of the mean (that is, between $8.31$ and $11.69$).

A clinical psychologist compares two therapy groups on a well-being scale. Both groups have a mean score of $10$. Group A has a standard deviation of $1.69$ and Group B has a standard deviation of $4.30$. The psychologist concludes that Group _____ demonstrates more consistent outcomes across patients, because its scores are more tightly clustered around the mean.

A social psychologist measures 'Community Engagement' scores (0–20 scale) in two neighborhoods. Both distributions have a mean of 10, but they look very different. Match each description or concept on the left to the correct value or definition on the right.

A researcher records scores on a 20-point sustained-attention task from two groups of participants. Both groups have a mean score of $10$. Match each term or description on the left to the correct interpretation on the right.

A researcher measures cognitive-load scores for two groups of participants. Both groups have a mean score of $10$, but Group A has a standard deviation of $1.69$ and Group B has a standard deviation of $4.30$. By analyzing these standard deviations, the researcher concludes that Group B exhibits greater _____ in its scores than Group A, because a larger standard deviation means individual scores differ from the mean by more units on average.

A researcher has collected scores on a psychological well-being scale from two independent samples. Both samples have a mean of $10$, but one has a standard deviation of $1.69$ and the other has a standard deviation of $4.30$. The researcher must evaluate which distribution provides more consistent scores and justify selecting it as the basis for a reliable measurement tool. Arrange the following steps in the order that best supports a well-reasoned evaluative conclusion.

Define standard deviation as described in the provided text. In your definition, refer to the example of two distributions with a mean of $10$ to explain what standard deviations of $1.69$ and $4.30$ recall about the average distance of scores from the mean.

Compare the distributions of anxiety scores between the two groups. Explain what these differing standard deviations reveal about how anxiety scores are spread around the mean of $10$ in each group, and specify which group has scores that are more tightly clustered near the center.

A psychologist comparing two memory training programs finds that participants in both groups have a mean score of $10$ on a recall test. However, Program X has a standard deviation of $1.69$ and Program Y has a standard deviation of $4.30$. If the psychologist wants to select the training program that produces the most consistent performance among participants, which program should they choose and why?