6.1 Statistical Measures

• Statistical measures provide insights into the central tendency, variability, and distribution of a dataset.


  True
• Match the statistical measure with its description:

  Mean ↔️ The average value in the dataset

  Median ↔️ The middle value when data is ordered

  Mode ↔️ The most frequently appearing value

  Range ↔️ The difference between highest and lowest values
• What does $x_{i}$ represent in the formula for the mean?


  Each individual value
• Match the statistical measure with its description:

  Mean ↔️ Average value

  Median ↔️ Middle value in ordered data

  Mode ↔️ Most frequently occurring value
• Statistical measures facilitate the comparison
• What is the first step in calculating the mean of a dataset?

  Add up all values
• $n$ in the mean formula refers to the total number of values in the dataset.


  True
• What is the formula for the mean, using mathematical notation?

  $\text{Mean} =$$\frac{\sum_{i = 1}^{n} x_{i}}{n}$
• To calculate the mean, you divide the sum of all values by the total number of values, which is denoted by n
• If there is an odd number of values in a dataset, the median is the middle
• What is the first step in calculating the mean of a dataset?

  Add up all values
• In the formula for the mean, what does $x_{i}$ represent?


  Each individual value
• If there is an even number of values, the median is the average of the two middle values.

  True
• To calculate the median, you must arrange the data in numerical order first.


  True
• A dataset is multimodal if multiple values have the same highest frequency.


  True
• Statistical measures provide insights into the central tendency and variability of a dataset.


  True
• Match the statistical measure with its description:

  Mean ↔️ The average value in the dataset

  Median ↔️ The middle value when the data is arranged in order

  Mode ↔️ The value that appears most frequently

  Range ↔️ The difference between the highest and lowest values
• What is the first step to calculate the median of a dataset?

  Arrange data in order
• What is the median of the dataset {2, 5, 7, 9, 12}?

  7
• What is the first step to calculate the mode?

  Arrange data in order
• The range of a dataset is the difference between the highest and lowest values
• In a frequency table, $f_{i}$ represents the frequency
• Match the statistical measure with its description:

  Mean ↔️ Average value

  Median ↔️ Middle value in ordered data

  Mode ↔️ Most frequently occurring value

  Range ↔️ Difference between highest and lowest values
• The median is the middle value in ordered
• If a dataset has an odd number of values, the median is the middle value.


  True
• The mode of a dataset is the value that appears most frequently
• The mean from the frequency table in the example is 4.9.


  True
• What is the first step in calculating the median from a frequency table?

  Arrange data in order
• What is the first step in calculating the mode from a frequency table?

  Identify highest frequency
• What role do frequencies play in calculating the median from a frequency table?

  Locate median value(s)
• The mean is always the best measure of central tendency when outliers are present.

  False
• The variance is the square root of the standard deviation.

  False
• A higher mean in one data set suggests its values are generally lower than another data set.

  False
• If Data Set B has a higher mean than Data Set A, its values are generally higher.


  True
• The median of the dataset {2, 5, 7, 9, 12} is the middle value, which is 7
• The median of the dataset {3, 5, 8, 10, 12, 15} is the average of 8 and 10, which is 9
• The mode of the dataset {3, 5, 2, 5, 7, 5, 2, 8} is 5
• Statistical measures facilitate the comparison of different datasets.
• What is the formula for the mean?

  $\text{Mean} =$$\frac{\sum_{i = 1}^{n} x_{i}}{n}$
• If a dataset has an odd number of values, the median is the middle value.


  True