1.5 Representing a Quantitative Variable with Graphs

• Continuous variables can take on any value within a range
• Stem-and-leaf plots are ideal for displaying the shape and range
• Discrete variables can only take specific, countable values.


  True
• What is the strength of a histogram?

  Shows frequency distribution
• What type of graph is used to explore relationships between two variables?

  Scatter plots
• Bar graphs have bars with no spacing between them.

  False
• Match the quantitative variable type with its histogram construction:

  Discrete ↔️ Bins correspond to specific values

  Continuous ↔️ Bins represent a range of values
• Discrete variables can only take on specific, countable values.


  True
• Line graphs are suitable for continuous variables but not for discrete variables.


  True
• What are quantitative variables?

  Variables with numerical values
• Match the variable type with an appropriate graph:

  Discrete ↔️ Bar graphs

  Continuous ↔️ Histograms
• Boxplots provide a detailed distribution of the data.

  False
• What type of variable is a histogram used for?

  Continuous
• What does the frequency in a histogram represent?

  Count of values in each bin
• To identify the appropriate graph types for quantitative variables, we need to distinguish between discrete and continuous variables.
• Continuous variables can take on any value within a range.
• Histograms are effective for visualizing the distribution of a single variable.
• What is a key difference between a histogram and a bar graph?

  Variable type
• What is the first step in creating a dot plot?

  Determine the range
• What is the median in a box plot?

  The middle value
• Box plots are only appropriate for continuous quantitative variables

  False
• Box plots are useful for comparing distributions across groups

  True
• Discrete variables are best represented using line graphs

  False
• Scatter plots are ideal for showing trends over time

  False
• Histograms may be less precise for small datasets


  True
• A histogram is a graphical representation that displays the distribution of a quantitative variable.
• What type of data is used to create bins in a histogram for a discrete variable?

  Specific, countable values
• How is frequency determined for bins in a histogram for a continuous variable?

  Count of values within each bin range
• Steps to create a dot plot

  1️⃣ Determine the range of data values

  2️⃣ Plot each data point as a dot
• Why are box plots useful for exploratory data analysis?

  Compact summary and outlier detection
• A symmetric histogram indicates that the data is evenly distributed around the mean.


  True
• What is the median in a box plot?

  Middle value of the data
• Steps to construct a histogram

  1️⃣ Bin the data into intervals

  2️⃣ Plot the frequency for each bin
• In a histogram, the bars are arranged in a fixed order.
• In a dot plot, each data point is plotted as a single dot.
• The quartiles in a box plot divide the data into four equal parts.
• The median is the middle value that divides the data in half
• Quantitative variables are variables that can take on numerical values
• Bar graphs are useful for comparing categorical data.
• For continuous quantitative variables, line graphs and scatter plots are suitable