b. Measures of Dispersion

• What do measures of dispersion describe in data analysis?

  Data points' deviation from average
• The range is the difference between the highest and lowest data points
• The standard deviation is the square root of the variance.
• What do dispersion measures focus on compared to measures of central tendency?

  Data variability
• Why are measures of dispersion essential in data analysis?

  Reveal spread of data
• A high standard deviation in test scores indicates students performed very differently
• Measures of dispersion can help identify outliers in data.
• What are the three main types of measures of dispersion?

  Range, variance, standard deviation
• Match the measure of dispersion with its description:

  Range ↔️ Difference between highest and lowest data points

  Variance ↔️ Average of squared differences from mean

  Standard Deviation ↔️ Square root of variance
• Steps to calculate variance

  1️⃣ Calculate the mean of the data

  2️⃣ Find the difference of each data point from the mean

  3️⃣ Square each difference

  4️⃣ Calculate the average of the squared differences
• The range is calculated as the highest data point minus the lowest data point
• Why is understanding measures of dispersion critical in data analysis?

  Insight into data variability
• Measures of dispersion can help identify outliers in data.
• Measures of dispersion indicate whether data points are closely clustered or widely scattered
• Match the measure of dispersion with its calculation:

  Range ↔️ $Highest \, Data \, Point - Lowest \, Data \, Point$

  Variance ↔️ $\frac{\sum{(x_{i} - \bar{x})^{2}}}{n}$

  Standard Deviation ↔️ $\sqrt{Variance}$
• What is the standard deviation the square root of?

  Variance
• Standard deviation is less sensitive to outliers than variance.
• What is the standard deviation equal to?

  Square root of variance
• The three primary measures of dispersion are range, variance, and standard deviation.
• The range is calculated by subtracting the lowest data point from the highest data point.
• What is variance defined as?

  Average squared difference from mean
• The standard deviation is less outlier-sensitive than variance.
• Match the measure of dispersion with its description:

  Range ↔️ Difference between extremes

  Variance ↔️ Average squared difference from mean

  Standard Deviation ↔️ Square root of variance
• Steps to calculate the range:

  1️⃣ Identify the highest data point

  2️⃣ Identify the lowest data point

  3️⃣ Subtract the lowest from the highest
• What values does the range use to measure spread?

  Extreme values only
• The interquartile range (IQR) measures the spread of the middle50% of a data set.
• The IQR is less sensitive to outliers than the range.
• What data does the IQR ignore when measuring spread?

  Data outside middle 50%
• Variance measures how much each data point deviates from the mean.
• What does the variance calculation amplify in the data?

  Outliers
• Variance is the foundation for calculating standard deviation.
• Standard deviation is the square root of the variance.
• What tool is required to calculate standard deviation accurately?

  Calculator
• Standard deviation focuses on data spread rather than its central location.
• Measures of dispersion describe the spread of data points around the average.
• Match the measure of dispersion with its formula:

  Range ↔️ $Range =$$Highest - Lowest$

  Variance ↔️ $Variance =$$\frac{\sum{(x_{i} - \bar{x})^{2}}}{n}$

  Standard Deviation ↔️ $Standard \, Deviation =$$\sqrt{Variance}$
• Why are measures of dispersion essential in data analysis?

  To reveal data variability
• A high standard deviation in test scores indicates students performed very differently.
• The three main types of measures of dispersion are range, variance, and standard deviation.
• What is the primary purpose of identifying outliers in data analysis?

  Spot unusual data points