Exploring One–Variable Data

Equal counts across stems may indicate uniformity that could mislead comparisons by suggesting similar distributions when differences exist.

Disparity in leaf unit sizes between plots might cause confusion regarding relative magnitudes within and across variables being compared.

Overlapping stems might create an illusion of similar variability even if other aspects of distributions differ significantly.

Skewedness in one or both distributions could make direct comparison difficult as it suggests non-similarity between groups.

Identical stems that confirm similarity in central location measurements.

Equal count of leaves across corresponding stems suggesting same variability.

Symmetric leaf arrangement reinforcing comparability of group distributions.

Variations in leaf spread on either side indicating skewness disparities.

Dotplot

Bar graph

Histogram

Stem-and-leaf plot

The median is closer to one end of the box than the other.

The whiskers are disproportionately long compared to the box.

The size of the box is nearly identical to the length of one whisker.

There's an unusually large gap between consecutive data points within the box.

Range

Median

Mean

Mode

Sports participation is unrelated to student's academic performance as measured by GPA.

Students with high GPAs are more likely to engage in sports than those with lower GPAs.

There may be an association between sports participation and GPA, but this doesn't mean participation causes higher GPAs.

Participation in sports leads directly to higher GPAs for students.

Single boxplot

Back-to-back stemplot

Histogram with non-overlapping intervals

Pie chart with percentages

Increasingly bi-modal distributions merely point out that more people are moving into middle-income brackets, signifying a positive development in the economy without further issues needing resolution.

Bi-modal distributions point towards an emerging divide in economic status with distinct groups reflecting different income levels. This indicates widening inequalities and has implications for economic policy or intervention.

These trends reflect normal fluctuations with no real connection to broader socioeconomic conditions or policymakers should not read into them too much, thereby maintaining the status quo approach.

No significant implications can be determined from changes in shape of distribution as it is likely due to random variance rather than any actual shift in economic situation.

Number of cars on a highway

Number of apples eaten

Time spent sleeping

Number of books read

Consistent distances between adjacent residual points suggest equal error variance but do not address whether there is a linear relationship present amongst variables analyzed via regression models.

A clear curve-like pattern within residuals suggests non-linearity between independent and dependent variables violating assumptions of linear regression model fitting.

Clusters of residuals at certain values indicate possible influential points but do not inherently violate linearity unless showing systematic curvature patterns.

Randomly scattered points generally centered around zero imply proper fit without systematic patterns indicating good adherence to linearity assumptions.