6.1 Statistical Measures

• What does the mean represent in a data set?

  The sum divided by values
• What is the median in a data set?

  The middle value
• What is the mode in a data set?

  The most frequent value
• What does the range measure in a data set?

  The spread of values
• The range is calculated by subtracting the lowest value from the highest value
• Standard deviation accounts for all data points in its calculation.

  True
• The second step to calculate the mean is to divide the sum by the number of values.
• To calculate the median, first order the numbers from smallest to largest.
• The mode is found by identifying the value that appears most frequently.
• The range is calculated as the difference between the highest and lowest values.
• Match the statistical measure with its description:

  Mean ↔️ Average of all values

  Median ↔️ Middle value in ordered data

  Mode ↔️ Most frequent value

  Range ↔️ Difference between highest and lowest values
• The range provides information about the central tendency of a data set.

  False
• What does standard deviation measure in a data set?

  Spread around the mean
• For the data set [2, 4, 6, 8], the variance is 5
• For the data set [2, 4, 6, 8], the variance is 5
• How is the mean calculated in a data set?

  Sum divided by values
• If there is an odd number of values, the median is the middle number
• To calculate the mean, you divide the sum of all values by the number of values.


  True
• The median is the middle value in a data set when arranged in ascending order.


  True
• Match the data set with its median:

  [3, 1, 6, 8, 7] ↔️ 6

  [2, 4, 6, 8] ↔️ 5
• If two or more values have the same highest frequency, the data set is called bimodal
• What does the standard deviation measure in a data set?

  Spread around mean
• What is the standard deviation for the data set [2, 4, 6, 8]?

  √5 ≈ 2.24
• Steps to calculate the standard deviation:

  1️⃣ Find the mean of the data set

  2️⃣ Subtract the mean from each data point to get deviations

  3️⃣ Square each deviation

  4️⃣ Calculate the average of the squared deviations (variance)

  5️⃣ Take the square root of the variance
• To calculate variance, you must square each deviation
• What does the interquartile range (IQR) represent?

  Middle 50% of data
• Match the statistical measure with its description:

  Range ↔️ Difference between highest and lowest values

  IQR ↔️ Difference between 75th and 25th percentiles

  Standard Deviation ↔️ Spread around the mean

  Variance ↔️ Average of squared deviations
• The IQR focuses on the middle 50%
• What is the mode in a data set?

  Most frequent value
• How is the range calculated in a data set?

  Highest minus lowest
• The average of squared deviations is called the variance
• What does the standard deviation measure in a data set?

  Spread or variability
• The range accounts for all data points in its calculation.

  False
• Steps to calculate the variance:

  1️⃣ Find the mean of the data set

  2️⃣ Subtract the mean from each data point to get deviations

  3️⃣ Square each deviation

  4️⃣ Calculate the average of these squared deviations
• The IQR is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). This measures the spread of the middle 50% of the data.
• The IQR is less affected by outliers than the range or standard deviation.

  True
• The mean is the same as the median in a symmetrical data set.


  True
• If a data set has an odd number of values, the median is the middle number.


  True
• A data set with no repeated values has no mode.


  True
• The range provides information about the variability of the data but not its central tendency.


  True