All MCQs

Aligned bar lengths are easier to compare accurately than angles or three-dimensional slices.
Sorting also helps viewers identify the largest and smallest shares.

Histogram intervals form a continuous numeric scale, so adjacent bins touch.
Bar-chart categories are discrete and are usually separated by gaps.

Bar charts encode category counts or values with separated bars.
Separation emphasizes that the categories are distinct rather than continuous intervals.

Very wide bins can hide modes and gaps, while very narrow bins can emphasize noise.
Analysts should examine reasonable alternative widths.

A frequency histogram counts observations within each interval.
The bar height therefore represents the bin frequency.

A histogram groups continuous values into intervals and displays their frequencies.
It reveals shape, spread, modes, gaps, and possible outliers.

Datasets with the same center may have different variability, skewness, or modality.
A useful summary usually combines center with spread and a distributional display.

Standard deviation measures spread, not center.
Equal means can therefore accompany very different levels of variability.

Trimming reduces the influence of the most extreme observations.
It provides a compromise between the efficiency of the mean and the robustness of the median.

Nominal categories have no meaningful numeric distances or order.
Counts and proportions directly describe how observations are distributed among categories.

Robust statistics remain reasonably stable under modest contamination or outliers.
The median and IQR are common examples.

Division by a zero or near-zero mean makes the ratio unstable.
A non-ratio scale also makes relative variation difficult to interpret.