6.1 Statistical Measures

• What are statistical measures used for?

  Summarizing or describing datasets
• The mode is the value that appears most frequently
• Statistical measures are numerical values that summarize or describe a dataset
• What does the range measure in a dataset?

  Spread of the data
• The mean is the average value calculated by summing all values and dividing by the total number of values
• How is standard deviation related to variance?

  It is the square root
• Different measures of central tendency and dispersion provide the same insights into a dataset.

  False
• Standard deviation is the square root of the variance
• Steps to calculate the mean of a dataset

  1️⃣ Sum all values

  2️⃣ Count the number of values

  3️⃣ Divide the sum by the count
• The mean, median, and mode are always the same value in a dataset.

  False
• How is the mean calculated?

  Sum values and divide
• What does standard deviation measure?

  Average deviation from mean
• The mode is always a unique value in a dataset.

  False
• What is the mean sensitive to in a dataset?

  Outliers
• The mode is the value that appears most frequently
• Steps to calculate the mean of the dataset: 75, 82, 90, 68, 88

  1️⃣ Sum the values: 75 + 82 + 90 + 68 + 88 = 403

  2️⃣ Count the number of values: 5

  3️⃣ Divide the sum by the count: 403 / 5 = 80.6
• What is the sum of the test scores \( 75, 82, 90, 68, 88 \)?

  403
• The median is more robust against outliers than the mean.


  True
• What is the range of the dataset \( 75, 82, 90, 68, 88 \)?

  22
• Match the statistical measure with its definition:

  Mean ↔️ The average value

  Median ↔️ The middle value

  Mode ↔️ The most frequent value

  Range ↔️ The difference between the highest and lowest values
• Steps to calculate the mean

  1️⃣ Sum the values

  2️⃣ Count the values

  3️⃣ Divide the sum by the count
• The mean test score for the given dataset is 80.6
• What does the mode represent in a dataset?

  The most frequent value
• The mean is sensitive to outliers
• The median is robust against outliers.


  True
• What does variance quantify?

  Data variability
• The first step in finding the median is to sort the data.


  True
• What is the mode for the dataset 75, 82, 90, 68, 82, 88?

  82
• Which measure is sensitive to outliers?

  Mean
• The median is the middle value when data is sorted in ascending order.


  True
• What is the purpose of using statistical measures in data analysis?

  To analyze and interpret data
• The median is affected by extreme values in a dataset.

  False
• Statistical measures provide a single way to understand the spread of a dataset.

  False
• Variance is the average squared deviation from the mean
• The range is a simple measure of dispersion that is easy to calculate
• How is variance calculated in a dataset?

  Squared deviation from mean
• What is the mean of the dataset: 75, 82, 90, 68, 88?

  80.6
• Steps to calculate the mean of a dataset

  1️⃣ Sum the values

  2️⃣ Count the number of values

  3️⃣ Divide the sum by the count
• What is the median of the dataset \( 75, 82, 90, 68, 88 \)?

  82
• The variance is the average squared deviation from the mean