C955 Applied Probability and Statistics - Set 4 - Part 1

Correct Answer: A histogram displays continuous numeric intervals; a bar chart displays categories

A histogram represents the distribution of a continuous variable using adjacent bars over numeric intervals, while a bar chart compares distinct categories with gaps between bars.

Correct Answer: The distribution's symmetry, skewness, and modality

A histogram reveals distributional features such as whether data is symmetric or skewed and whether it has one peak or several.

Correct Answer: One with a long tail extending toward higher values

A right-skewed (positively skewed) distribution has most values clustered low with a long tail of high values pulling the mean rightward.

Correct Answer: One with a long tail extending toward lower values

A left-skewed (negatively skewed) distribution has a long tail of low values, so the mean is pulled below the median.

Correct Answer: A distribution with two distinct peaks

A bimodal distribution has two prominent peaks, which often indicates that the data combine two different underlying groups.

Correct Answer: A value that lies far from the bulk of the data

An outlier is an observation markedly distant from the rest of the data, which may reflect a genuine extreme, a data entry error, or a different process.

Correct Answer: Q1 minus 1.5 IQR or Q3 plus 1.5 IQR

The common rule flags values below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR as potential outliers.

Correct Answer: They may represent genuine important observations or reveal errors

An outlier might be a legitimate extreme value carrying important information or a data error. Investigating the cause guides whether removal is justified.

Correct Answer: The relationship between two numeric variables

A scatterplot plots paired observations of two numeric variables, revealing the form, direction, and strength of any relationship between them.

Correct Answer: A positive association

Points rising from left to right indicate a positive association, meaning that as one variable increases the other tends to increase as well.

Correct Answer: Describing a distribution using minimum, Q1, median, Q3, and maximum

The five-number summary captures the center, spread, and range of a distribution and provides the values used to construct a box plot.

Correct Answer: The percentage of values at or below a given value

A value's percentile rank indicates the percentage of the data that falls at or below it, so the 90th percentile exceeds 90 percent of observations.

Correct Answer: They scored higher than about 75 percent of the group

A 75th percentile score means the student performed better than roughly 75 percent of the reference group, regardless of the raw score value.

Correct Answer: The 50th percentile

The median divides the data in half, so it corresponds to the 50th percentile with half the values below it.

Correct Answer: Comparing relative variability between data sets with different units or scales

The coefficient of variation expresses standard deviation as a percentage of the mean, allowing comparison of relative spread across data sets on different scales.

Correct Answer: The mean describes center but not variability

The mean summarizes only the center. Data sets with identical means can differ greatly in how spread out their values are, which measures of spread capture.

Correct Answer: A summary showing how often each value or interval occurs

A frequency distribution organizes data by showing the count of observations falling into each value or interval, revealing the overall pattern.

Correct Answer: The proportion of observations in a category

Relative frequency is a category's count divided by the total, expressing how common the category is as a proportion or percentage.

Correct Answer: The running total of frequencies up to a given value

Cumulative frequency accumulates counts up through each value or interval, useful for finding percentiles and the number of observations below a threshold.

Correct Answer: Manipulated axes or scales can exaggerate or hide real patterns

Truncated axes, inconsistent scales, or omitted context can make differences appear larger or smaller than they are, distorting the reader's conclusions.