1.8 Graphical Representations of Summary Statistics

• What is the definition of the mean in summary statistics?

  The average value
• Match the summary statistic with its usefulness:

  Mean ↔️ Indicates the central tendency

  Median ↔️ Reflects the central value, less influenced by outliers

  Standard Deviation ↔️ Indicates the variability of data points

  Range ↔️ Simple measure of spread
• The standard deviation measures the spread or dispersion of data around the mean.

  True
• Match the graphical representation with its strength:

  Dot plots ↔️ Clear representation of individual data points

  Histograms ↔️ Effective for large datasets and continuous data

  Box plots ↔️ Summarizes key percentiles
• Box plots are useful for comparing distributions and identifying outliers.


  True
• Box plots show the frequency of individual data points.

  False
• Match the summary statistic with its definition:

  Range ↔️ Difference between largest and smallest values

  Variance ↔️ Average squared deviation from the mean

  Standard Deviation ↔️ Square root of the variance
• What is the range for the dataset [2, 4, 6, 8, 10]?

  8
• Dot plots are useful for large datasets or continuous data.

  False
• Match the summary statistic with its definition in a box plot:

  Median ↔️ Middle value of the dataset

  Q1 ↔️ 25th percentile of the data

  Q3 ↔️ 75th percentile of the data
• Box plots summarize the spread of data using key percentiles.


  True
• Dot plots display individual data points as dots along a number line.


  True
• Box plots provide a concise summary of the key statistics in a dataset.


  True
• Dot plots provide a more detailed view of the data distribution than box plots.

  True
• Box plots hide the individual data points in a dataset.


  True
• What does the box in a box plot represent?

  Middle 50% of the data
• The median is the middle value when the data is arranged in order
• What does the mean indicate in a dataset?

  The central tendency
• What is a weakness of dot plots when dealing with large datasets?

  They become cluttered
• Dot plots are effective for showing the summary statistics of a dataset.


  True
• Match the graphical representation with its strength:

  Dot plots ↔️ Clear representation of individual data points

  Histograms ↔️ Effective for large datasets

  Box plots ↔️ Summarizes key percentiles
• Histograms are effective for showing distribution shapes but do not display individual data points
• The minimum in a box plot is the smallest value in the dataset.

  True
• Summary statistics are numerical measures that describe the central tendency and spread of a dataset
• The range is the difference between the largest and smallest values
• Why is the median less influenced by outliers than the mean?

  It uses the middle value
• How is the mean represented in a dot plot?

  Average position of dots
• The median in a box plot represents the 50th percentile.
• Box plots are particularly useful for identifying outliers
• The median is the middle value when the data is arranged in order
• The standard deviation measures the variability of data points around the mean.


  True
• Match the summary statistic with its representation in a dot plot:

  Mean ↔️ Average position of the dots

  Median ↔️ Middle dot when data is in order

  Mode ↔️ Point with highest dot concentration
• Box plots display five summary statistics, including the minimum, Q1, median, Q3, and maximum
• Dot plots are strong at identifying data clusters
• What are the two main graphical representations used to compare summary statistics across different datasets?

  Dot plots and box plots
• For what type of datasets are dot plots most useful?

  Small datasets
• What do the whiskers in a box plot represent?

  Minimum and maximum values
• A box plot of Dataset A would show the median at 4.5
• Dot plots allow you to identify the mean, median, and mode
• The mean is calculated by summing all values and dividing by the total number of values.


  True