7.5.1.2 Measures of Dispersion

• What is the purpose of measures of dispersion in statistics?

  Describe data point spread
• Measures of dispersion contrast with measures of central tendency
• The range is calculated by adding the highest and lowest values in a dataset.

  False
• What is the formula for calculating standard deviation?
• Match the measure of dispersion with its advantage:

  Range ↔️ Easy to calculate and understand

  Standard deviation ↔️ Accounts for all values in dataset
• To calculate the range, you subtract the lowest value from the highest value.
• Steps to calculate the standard deviation of a dataset

  1️⃣ Calculate the mean of the dataset

  2️⃣ Find the deviation of each value from the mean

  3️⃣ Square each deviation

  4️⃣ Calculate the variance

  5️⃣ Take the square root of the variance
• What is the mean of the dataset {2, 4, 6}?

  4
• The standard deviation of the dataset {2, 4,6} is approximately 1.63
• Measures of dispersion describe how much data points are spread out around the central value in a dataset.
• Match the measure of dispersion with its description:

  Range ↔️ Difference between highest and lowest values

  Standard deviation ↔️ Measure of data dispersion around mean
• Measures of dispersion highlight the variability
• Measures of dispersion focus on typical values in a dataset.

  False
• What is the central value in a dataset referred to in the context of measures of dispersion?

  Mean
• The range is calculated by subtracting the lowest value from the highest value
• Standard deviation is the square root of the variance.
• What does standard deviation measure?

  Data dispersion
• Match the measure of dispersion with its definition and calculation:

  Range ↔️ Difference between highest and lowest values ||| Highest value - Lowest value

  Standard Deviation ↔️ Square root of the variance |||
• The formula for calculating the range is Highest value - Lowest value
• The range provides detailed information about data variability.

  False
• Why is the range affected by outliers?

  It uses extreme values
• To calculate the mean, you sum all values and divide by the number of data points
• Variance is calculated by summing squared deviations and dividing by N.
• What is the approximate standard deviation of the dataset {2, 4, 6}?

  1.63
• Variance measures the average of the squared differences from the mean
• Variance can be negative if the data values are negative.

  False
• Steps to calculate the standard deviation of a dataset:

  1️⃣ Calculate the mean

  2️⃣ Find the deviation of each value from the mean

  3️⃣ Square each deviation

  4️⃣ Calculate the variance

  5️⃣ Take the square root of the variance
• The squared deviation is calculated as (x_{i} - \mu)^{2}
• Variance measures the average of the squared differences from the mean.
• Steps to calculate variance

  1️⃣ Find the mean (\mu</latex>) of the dataset

  2️⃣ Calculate the deviation of each value from the mean ()

  3️⃣ Square each deviation ()

  4️⃣ Sum the squared deviations and divide by :
• The formula to calculate variance is \frac{\sum (x_{i} - \mu)^{2}}{N}
• Match the step in calculating variance with its description:

  Find the mean ↔️ Calculate the average of the dataset

  Calculate the deviation ↔️ Subtract the mean from each value

  Square the deviation ↔️ Multiply the deviation by itself

  Sum and divide ↔️ Calculate the final variance
• The first step in calculating variance is to find the mean
• Deviation is calculated by subtracting the mean from each data value.
• Squaring each deviation ensures that all values are positive.
• Variance is calculated by dividing the sum of squared deviations by N
• Steps to calculate variance

  1️⃣ Find the mean of the dataset

  2️⃣ Calculate the deviation of each value from the mean

  3️⃣ Square each deviation

  4️⃣ Sum the squared deviations

  5️⃣ Divide the sum by N
• What does variance measure in a dataset?

  Squared differences from the mean
• To calculate variance, sum the squared deviations and divide by N
• The first step in calculating variance is to find the mean of the dataset.