Examples of Low and High Variability

What does the variability of a set of scores describe?

In a psychological study, if two different groups of participants have identical average scores, they will also necessarily have the same degree of variability in their results.

Rank the following research study outcomes in order from the distribution with the lowest variability (1) to the distribution with the highest variability (3).

In psychological statistics, the term 'variability' describes the extent to which individual scores in a distribution differ or spread out around the average.

A psychology researcher finds that two groups of participants have the same mean score of $50$ on a memory task, but Group A has much higher variability than Group B. What does this indicate about the scores in Group A?

A psychologist evaluates two clinical trials that both achieved an average improvement score of $20$ points. Trial A has scores that cluster tightly around the average, while Trial B has scores ranging widely from $5$ to $40$ points of improvement. The psychologist judges the average for Trial B to be misleading when predicting individual outcomes because of the high _____ within its distribution.

A psychology researcher measures the reaction times (in milliseconds) for three different groups. All three groups have an identical mean reaction time of $400$ ms, but their distributions differ. Match each group's scores to the analytical conclusion that best describes its variability and the representativeness of the mean.

A cognitive psychologist measures the number of words recalled from a list of $20$ items by participants in three different study conditions. In all three conditions, the average (mean) recall score is exactly $12$ words. Match each condition's actual dataset to the description of its variability relative to the others.

A developmental psychologist is studying the age (in months) at which infants first begin to walk. She compares two distinct groups of infants:

• Group 1: ages are $[9, 10, 11, 12, 13]$ months, with a mean of $11$ months.
• Group 2: ages are $[6, 8, 11, 14, 16]$ months, with a mean of $11$ months.

When analyzing these datasets, the psychologist notes that while the central tendency is identical, the individual scores in Group 2 are far more dispersed. To determine which group's average is a more reliable predictor of an individual infant's developmental milestone, the researcher must analyze the statistical ____ of each distribution, since a higher degree of this spread indicates that individual scores differ more dramatically from the group average.

A research team is evaluating three different psychological datasets to determine how well each group's mean represents the performance of individual participants.

Arrange these research scenarios in order from the dataset where the group mean is the least representative (highest variability) of individual scores to the dataset where the group mean is the most representative (lowest variability) of individual scores.