1.9 Comparing Distributions of a Quantitative Variable

• A quantitative variable can take on numerical values
• Standard deviation is the square root of the variance
• The mean is one measure of the center
• What does the shape of a distribution describe?

  The overall form
• Match the measure with its description:

  Range ↔️ The difference between the highest and lowest values

  Variance ↔️ The average squared deviation from the mean

  Standard Deviation ↔️ The square root of the variance
• What two measures are commonly used to compare distributions of a quantitative variable?

  Median and standard deviation
• What is a quantitative variable?

  A variable with numerical values
• How is the mean calculated in a distribution?

  Sum of values divided by number of values
• What two aspects of a distribution does analyzing measures of center and spread help describe?

  Typical values and dispersion
• The standard deviation is the square root of the variance
• When comparing distributions, the measure of spread with the larger value indicates greater variability
• Variance measures the average squared deviation from the mean.


  True
• Steps to compare distributions of a quantitative variable:

  1️⃣ Compare the shape

  2️⃣ Compare the center

  3️⃣ Compare the spread
• Two key measures to compare distributions are the median and standard deviation
• The mean of a dataset is its average
• Comparing measures of center and spread allows you to identify similarities and differences in data patterns.

  True
• Comparing the median and standard deviation identifies differences in the typical values and the spread of the data
• The standard deviation is the square root of the variance
• The variance is calculated by summing the squared deviations from the mean
• Match the measure of center with its description:

  Mean ↔️ Average value

  Median ↔️ Middle value when ordered

  Mode ↔️ Most common value
• A larger standard deviation indicates data is more dispersed.


  True
• The median is the middle value when the data is ordered
• The mean is the only measure of center.

  False
• The range is the difference between the highest and lowest values in a dataset.

  True
• A unimodal distribution has two peaks.

  False
• The standard deviation measures the spread of the data around the mean
• The median represents the typical or central value of a dataset.


  True
• The range is the average squared deviation from the mean.

  False
• The mode is the most frequently occurring value in a dataset.


  True
• Order the key characteristics of shape in a distribution:

  1️⃣ Symmetry

  2️⃣ Skewness

  3️⃣ Unimodal vs. Bimodal
• What does the standard deviation measure in a distribution?

  Dispersion around the mean