Data Displays
Which visual display is most appropriate to present the distribution of a categorical variable such as preferred blood type or habitat location?
What is a Bar Graph (or Pie Chart)?
Explanation: Bar graphs show categorical counts with distinct gaps between bars. Histograms, dotplots, and boxplots are reserved strictly for quantitative data.
What is the difference between mean and median?
Mean is the average, and median is the middle number
What is the range of a data set?
The maximum minus the minimum.
In a data set of 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 15, which number is the outlier?
15
What is gained by selecting a sample using random selection from a population?
What is Generalization to the larger population?
Explanation: Random sampling ensures the sample is representative of the population, allowing results to be generalized.
What percentage do the slices of a pie chart have to add up to?
100%
What is Q1?
The median of the bottom half of the data.
The IQR (interquartile range), represents the middle what percent of the data?
The middle 50%
What is the formula to calculate the Upper Boundary threshold for high outliers?
Q3 + 1.5 X IQR
What essential experimental component is required to establish a direct cause-and-effect relationship between variables?
What is Random Assignment of experimental units to treatments?
Explanation: Random assignment balances potential confounding variables across treatment groups, isolating the cause.
Unlike a histogram, which specific advantage does a dotplot hold when displaying small quantitative datasets?
What is retaining actual individual data values?
Explanation: Histograms group data into bin intervals, losing individual point values. Dotplots preserve every raw data entry while showing shape.
What percentage of the data is below Q3?
75%
The typical distance that data points are from the mean is called what?
Standard deviation
A dataset has Q1 = 65 and Q3 = 81. Using the 1.5 x IQR rule, what numerical threshold determines if a low score is a low outlier?
Below 41.0
Q1 - 1.5 (IQR)
65 - 1.5(16)
An observational study finds that people who drink green tea have lower heart disease rates. Why can't researchers claim green tea causes lower heart disease?
What are confounding variables?
Explanation: Without random assignment (it's an observational study), confounding variables like exercise or diet habits cannot be ruled out.
When the data resembles a curve with the same number of points on either side of the median the same distance from the median, this data is called what?
Symmetric
If a quantitative distribution of exam scores is strongly skewed to the left, what is the expected relationship between the Mean and the Median?
What is Mean < Median?
Explanation: Extreme low values pull the non-resistant mean downward toward the long left tail, making it smaller than the median.
Between IQR and Standard deviation, which one should you use for data that is skewed left or right?
Use IQR because it is resistant to skew and outliers.
If an extreme high outlier is removed from a dataset, what happens to the values of the Mean, Standard Deviation, and Median?
What is Mean & SD decrease; Median remains virtually unchanged?
Median is resistant to outliers, mean and SD are affected.
If an advertisement double-scales both the height AND width of a graphic icon to show a 2-fold increase, by what factor does the visual area increase?
What is a factor of 4 (Quadrupling)?
Explanation: Area scales quadratically (2^2 = 4). Violating the Area Principle misleads viewers into perceiving a 4-fold increase instead of 2-fold.
20-40
If a quantitative distribution of exam scores is symmetric what is the expected relationship between the Mean and the Median?
How do you calculate the standard deviation?
The square root of the sum of the squares of distances each data point is from the average divided by the number of values minus 1.
Which pair of summary statistics is most appropriate to report when describing a heavily right-skewed salary distribution with several high outliers?
What are the Median and Interquartile Range (IQR)?
Explanation: Median and IQR are resistant measures that remain stable in the presence of skewness and extreme values.
A news graphic shows bar heights for candidate support jumping from 48% to 52%, but the vertical axis starts at 45%. Why is this misleading?
What is the difference is exaggerated?
Explanation: Truncating the y-axis away from zero visually exaggerates minor difference (4%) into making one bar look more than twice as tall.