1.7 Summary Statistics for a Quantitative Variable

• The median is affected by extreme values in a dataset.

  False
• The mode is the only measure of central tendency that can be used for both quantitative and qualitative
• The range is a measure of dispersion
• What does the median represent in a dataset?

  Middle value
• What is the median in this example?

  9
• The mode can be used for both quantitative and qualitative data
• The mean is affected by outliers.


  True
• What is the range of the dataset: 5, 8, 10, 12, 15?

  10
• What is the 1st quartile (Q1) in a dataset?

  Lower half median
• Which measure of dispersion is least affected by outliers?

  IQR
• How does the standard deviation compare to the range in terms of outlier effect?

  Less affected by outliers
• Steps to calculate the standard deviation of a dataset.

  1️⃣ Calculate the mean

  2️⃣ Subtract the mean from each data value

  3️⃣ Square each of the deviations

  4️⃣ Sum the squared deviations

  5️⃣ Divide the sum by the number of values

  6️⃣ Take the square root of the result
• Match each measure of dispersion with its definition and usefulness.

  Range ↔️ Max - Min ||| Quick overview of spread

  Interquartile Range (IQR) ↔️ Q3 - Q1 ||| More robust against outliers

  Standard Deviation ↔️ Average deviation from mean ||| Comprehensive measure
• Steps to calculate the mean of a dataset.

  1️⃣ Sum all the values in the dataset

  2️⃣ Divide the sum by the number of values
• Steps to find the median of a dataset.

  1️⃣ Sort the data in ascending order

  2️⃣ Identify the middle value
• What is the median of a dataset when it is sorted in ascending order?

  Middle value
• Which measure of central tendency identifies the most frequently occurring value in a dataset?

  Mode
• Match the measure of dispersion with its definition:

  Range ↔️ Max - Min

  IQR ↔️ Q3 - Q1

  Standard Deviation ↔️ Average deviation from mean
• Arrange the quartiles in the correct order:

  1️⃣ Q1

  2️⃣ Q2

  3️⃣ Q3
• The standard deviation is affected moderately by outliers.


  True
• What does standard deviation measure in a dataset?

  Spread of data
• The sum of squared deviations is divided by the number of values to calculate standard deviation.


  True
• The range is highly affected by outliers.


  True
• The formula for variance involves taking the square root of the squared deviations.

  False
• Which measure of central tendency is most influenced by outliers?

  Mean
• What is the mean often called in statistics?

  Average
• Match the measure of central tendency with its definition:

  Mean ↔️ The average value

  Median ↔️ The middle value when sorted

  Mode ↔️ The most frequent value
• The range is highly affected by outliers.


  True
• The median provides a more stable representation of the central value when outliers are present in the dataset.
• The median is more affected by outliers than the mean.

  False
• The mode is affected by outliers.

  False
• The range is a measure of dispersion
• Steps to calculate the range

  1️⃣ Identify the maximum value

  2️⃣ Identify the minimum value

  3️⃣ Subtract the minimum value from the maximum value
• The interquartile range (IQR) is calculated as Q3 minus Q1
• What does the standard deviation measure in a dataset?

  Average deviation from mean
• The standard deviation formula involves taking the square root of the variance
• In the formula for standard deviation, $\bar{x}$ represents the mean
• To calculate the standard deviation, you divide the sum of squared deviations by the number of values
• The standard deviation is more sensitive to outliers
• The mean of the dataset 5, 8, 10, 12, 15 is 10