1.6 Describing the Distribution of a Quantitative Variable

• Quantitative variables are variables that can take on numerical values and represent a measurable quantity
• Discrete quantitative variables have a finite set of possible values.


  True
• The median is robust to outliers, making it suitable for skewed distributions.

  True
• A symmetric distribution has data evenly distributed around the center.


  True
• What is the formula for calculating the range of a dataset?

  Max - Min
• The interquartile range is calculated as Q3 - Q1
• Histograms group data into bins and show the frequency within each bin.
• Continuous quantitative variables can take on any value within a range
• The mean is best for symmetric distributions but is sensitive to outliers
• Arrange the steps to calculate the mean of a dataset:

  1️⃣ Sum all values

  2️⃣ Divide the sum by the number of values
• Match the measure of spread with its definition:

  Range ↔️ The difference between the maximum and minimum values

  IQR ↔️ The range of the middle 50% of the data

  Standard Deviation ↔️ The average distance from the mean
• The standard deviation provides a detailed picture of variability in a dataset.


  True
• The standard deviation provides an intuitive measure of spread in the original units of the data.


  True
• Match the data representation method with its feature:

  Histogram ↔️ Frequency of values in bins

  Dot Plot ↔️ Individual data points
• Discrete quantitative variables can only take specific, countable values
• The mean is the best measure of center for skewed distributions.

  False
• What does the variance measure in statistics?

  Average squared deviation
• What does a histogram show about data?

  Frequency in intervals
• Dot plots are particularly useful for smaller datasets
• Match the distribution shape with its characteristic:

  Symmetric ↔️ Mean ≈ Median

  Skewed Left ↔️ Mean < Median

  Skewed Right ↔️ Mean > Median
• Why is identifying outliers important in data analysis?

  Skews measures of center
• What is the best measure of center for symmetric distributions?

  Mean
• Discrete quantitative variables can only take on specific, countable values.

  True
• What are the three main measures of center for quantitative data?

  Mean, median, and mode
• Match the measure of center with its definition:

  Mean ↔️ The average value

  Median ↔️ The middle value

  Mode ↔️ The most frequent value
• The median is the best measure of center for a skewed
• The IQR is robust to outliers and useful for skewed distributions.
• The standard deviation is the square root of the variance
• Dot plots are particularly useful for smaller datasets because they preserve individual data points.


  True
• Both histograms and dot plots can provide valuable insights into the distribution of a quantitative variable.


  True
• A symmetric distribution has its mean approximately equal to its median
• The standard deviation is the square root of the variance and provides an intuitive measure of spread in the original units.


  True
• If the scores of students are [70, 80, 90, 100], the range is 30.

  True
• What does the bin size determine in a histogram?

  Level of detail
• What are the three common types of distribution shapes?

  Symmetric, skewed left, skewed right
• In a symmetric distribution, the mean is approximately equal to the median.


  True
• The median is the best measure of center for skewed distributions.


  True
• A histogram's bin size determines the level of detail
• Continuous quantitative variables can take any value within a range.


  True
• The median is robust to outliers