Two distributions of scores can have the same mean, median, and mode but still differ in how spread out the individual scores are around the center.

The provided image displays two distributions that share the same mean, median, and mode. Based on the visual spread of the scores, which of the following is a correct interpretation of their variability?

A psychology researcher is analyzing the test scores of three different groups. In all three groups, the mean score is exactly 80%. Based on the distribution of scores provided below, arrange the groups in order of their variability, starting with the group that demonstrates the lowest variability and ending with the group that demonstrates the highest variability.

• Group X: Scores are {79%, 80%, 81%}
• Group Y: Scores are {60%, 80%, 100%}
• Group Z: Scores are {70%, 80%, 90%}

When comparing two score distributions that share the exact same central tendency (such as a mean, median, and mode of $10$), which of the following correctly describes how they differ in their variability?

If two different groups of study participants share the exact same central tendency on a memory test (with a mean, median, and mode of $10$), it guarantees that both groups will also have the same spread of scores close to that average.

A researcher is critiquing a report that describes two different patient groups as 'equivalent' simply because they share an identical mean recovery time of $14$ days. The researcher argues that this evaluation is flawed because it ignores the _____ of the distributions, which would reveal if one group has much more inconsistent recovery times than the other.

Two distributions both have a mean, median, and mode of $10$ but look very different when graphed. Match each term on the left with the description on the right that best fits it.

A researcher is reviewing four study scenarios, each involving score distributions with a mean of $10$. Match each scenario on the left to the conclusion about variability that a researcher would correctly apply.

A researcher examines quiz scores from two classrooms. Classroom A's scores are $\{9, 10, 10, 10, 11\}$ and Classroom B's scores are $\{2, 6, 10, 14, 18\}$. After computing the central tendency, the researcher finds the mean, median, and mode are identical across both classrooms. The researcher then analyzes the spread of the scores and concludes that Classroom B has _____ variability than Classroom A.

A researcher wants to evaluate whether two groups of participants are truly equivalent in their performance on a cognitive task. Both groups have a mean score of $10$. Arrange the following reasoning steps in the order that produces the most rigorous and defensible evaluation of group equivalence.

Based on the concept of variability, define how a distribution with relatively low variability and a distribution with relatively high variability differ in terms of their scores' locations relative to their central tendency, even when both distributions share the exact same mean, median, and mode of $10$.

Using the concepts of central tendency and variability, explain how the researcher should interpret and compare the spread of reaction times in Group A and Group B, and explain why relying solely on central tendency would lead to an incomplete understanding of the two groups' performances.

Imagine you are comparing two psychology class exam distributions. Both classes have a central tendency (mean, median, and mode) of $10$ points on a quiz, but Class X has low variability while Class Y has high variability. In which class would you expect to find a student score of $3$ points, and why?