6.1 Statistical Measures

• The standard deviation is the square root of the variance.
• The mean is calculated by summing all values and dividing by the total number of values
• What does the median represent in a dataset?

  Middle value
• The mode is the value that appears most frequently in a dataset.
• The range is the difference between the highest and lowest values
• What does the variance measure in statistics?

  Spread of data
• The standard deviation is the square root of the variance.
• The standard deviation is the square root of the variance
• Measures of dispersion provide information about the spread of data around its central tendency.
• The range is calculated as the difference between the highest and lowest values in the dataset
• What is statistics primarily concerned with?

  Analyzing and interpreting data
• Statistics helps identify patterns and trends in data.
• The mean is calculated by summing all values and dividing by the total number of values
• What is the median in a dataset?

  The middle value
• The variance is the average squared deviation from the mean
• What is the main purpose of measures of central tendency?

  Describe the typical value
• The mean, median, and mode provide different ways to understand the central tendency of data.
• The formula for the range is the highest value minus the lowest
• What does a higher standard deviation indicate about a dataset?

  Greater data variability
• Arrange the measures of position from lowest to highest division of data.

  1️⃣ Deciles

  2️⃣ Percentiles

  3️⃣ Quartiles
• The third quartile (Q3) represents the 75th percentile of a dataset.
• What do percentiles divide a dataset into?

  100 equal parts
• The first quartile (Q1) corresponds to the 25th percentile.
• Which decile represents the 90th percentile?

  D10
• Measures of position are used to complement measures of central tendency and dispersion.
• For what purpose is the mean most useful in statistical analysis?

  Calculating the average value
• The median is less affected by outliers than the mean.
• Match the measure of central tendency with its use:

  Mean ↔️ Calculate the average value

  Median ↔️ Identify the middle value

  Mode ↔️ Identify the most frequent value
• What does the range measure in a dataset?

  The overall spread of data
• The variance provides a detailed measure of how spread out the values are from the mean.
• The standard deviation expresses the average amount of deviation from the mean in the same units as the original data.
• Order the measures of dispersion from least to most detailed:

  1️⃣ Range

  2️⃣ Variance

  3️⃣ Standard Deviation
• In a dataset of exam scores, what does a mean of 75 indicate?

  The typical performance level
• In a dataset of exam scores, what does a range of 40 suggest about the data?

  A wide spread of scores
• In a dataset of exam scores, what does a variance of 64 indicate?

  Moderate deviation from the mean
• A standard deviation of 8 in exam scores means most scores fall within 8 points of the average.
• What decisions can statistical measures inform in education?

  Teaching methods and exam difficulty
• What is the study of collecting, organizing, analyzing, and interpreting data called?

  Statistics
• Statistics allows us to describe and summarize data
• Statistics is used to make predictions based on data.