6.1 Statistical Measures

• Match the type of statistical measure with its purpose:

  Mean ↔️ Describes the average value

  Median ↔️ Identifies the middle value

  Mode ↔️ Finds the most frequent value

  Range ↔️ Measures the spread of data
• Statistical measures are methods to describe the central tendency and spread of a data set.
• What is the formula for calculating the mean?

  $\frac{\sum x}{n}$
• The median is always the middle value of a data set without sorting.

  False
• The mode is the most frequent value in a data set.
• What is the formula for calculating the range?

  $x_{\max} - x_{\min}$
• The mean is calculated by summing all values and dividing by the number of values.
• What is the range of the data set {2, 4, 6}?

  4
• The mean of the data set {2, 4, 6} is 4.
• If a data set has an odd number of values, the median is the middle value.
• What is the median of the data set {2, 4, 6}?

  4
• What is the median of the data set {2, 4, 6}?

  4
• Match the statistical measure with its example:

  Mean ↔️ Mean of {2, 4, 6}: 4

  Median ↔️ Median of {2, 4, 6}: 4

  Mode ↔️ Mode of {2, 4, 4, 6}: 4
• The median of the data set {2, 4, 6} is 4.


  True
• What is the mode of the data set {2, 4, 4, 6}?

  4
• Steps to find the median of a data set:

  1️⃣ Arrange the data in order

  2️⃣ Identify the middle value
• The IQR is the difference between Q3 and Q1.
• What does the mean represent in statistical measures?

  Average of all data
• How is the mean calculated?

  Sum of values / number of values
• The formula for the mean is \frac{\sum x}{n}.
• The median is the middle value in a sorted dataset.


  True
• What is the mean of the dataset {2, 4, 6}?

  4
• Steps to find the median of a dataset

  1️⃣ Arrange the data in order

  2️⃣ Identify the middle value
• If a dataset has an odd number of values, the median is the middle value.
• If a dataset has an even number of values, the median is the average of the two middle values.
• What is the median of the dataset {2, 4, 6}?

  4
• The median of {1, 3, 5, 7} is 4.


  True
• Steps to determine the mode of a dataset

  1️⃣ Identify unique values

  2️⃣ Count the frequency of each value

  3️⃣ The highest frequency value is the mode
• What is a multimodal dataset?

  Multiple values with the same highest frequency
• Match the statistical measure with its characteristic:

  Mean ↔️ Sensitive to outliers

  Median ↔️ Robust to outliers

  Mode ↔️ Represents most common value
• What is the outlier in the dataset {2, 4, 6, 8, 10, 30} using the IQR method?

  30
• Outliers can significantly affect the mean of a dataset.
• What does IQR stand for in statistics?

  Interquartile Range
• The upper bound for outlier detection is calculated using Q3 + 1.5 * IQR.


  True
• Steps to identify outliers in a data set

  1️⃣ Determine Q1 and Q3

  2️⃣ Calculate IQR

  3️⃣ Calculate Lower Bound

  4️⃣ Calculate Upper Bound

  5️⃣ Identify values outside bounds
• The median is less affected by outliers and remains representative of central tendency
• What are common statistical measures for describing central tendency?

  Mean, median, mode
• Match the statistical measure with its description:

  Mean ↔️ Average value

  Median ↔️ Middle value

  Mode ↔️ Most frequent value

  Range ↔️ Highest minus lowest
• The median is always equal to the mean in a symmetrical data set.

  False
• What does 'n' represent in the formula for calculating the mean?

  Number of values