Research methods 4

• What is the purpose of summarizing data?


  To simplify complex data and make it easier to understand
• What does a measure of central tendency indicate?


  It provides an indication of a "typical" score in the data set
• What are the three common measures of central tendency?

  • Mean
  • Median
  • Mode
• How do you calculate the mean of a data set?


  Add all scores together and divide by the number of scores (N)
• What is the mean of the data set {4, 5, 1, 1, 10, 7, 11, 1}?


  $5$
• What is a pro of using the mean as a measure of central tendency?


  It provides an estimate of the average score in the data set
• What is a con of using the mean?


  It is affected by extreme data points
• How do you find the median of a data set?


  Order the data and find the value in the middle
• What is the median of the ordered data set {1, 1, 1, 4, 5, 7, 10, 11}?


  $4.5$
• What is a pro of using the median?


  It is insensitive to extreme scores in the data set
• What is a con of using the median?


  It doesn’t reflect the shape of the scores
• What is the mode in a data set?


  The most frequently occurring score
• What is the mode of the data set {4, 5, 1, 1, 10, 7, 11, 1}?


  $1$
• What is a pro of using the mode?


  It is easy to calculate and understand
• What is a con of using the mode?


  The data set might have more than one mode or no mode at all
• When should you use the mean, median, or mode?


  • Use the mean for normally distributed data
  • Use the median for skewed data
  • Use the mode for categorical data or when the most common value is needed
• What is the data set representing hours spent watching TV last night?


  {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}
• What are the three data sets provided as examples for measures of central tendency?


  1. {1, 1, 1, 2, 2, 3, 4, 5, 5, 6}
  2. {1, 27, 28, 29, 30}
  3. {1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 50}
• What does "spread" refer to in a data set?


  It refers to how spread out the data is.
• What is the summary of the three common measures of central tendency?

  Mean: average of scores; Median: middle score; Mode: most frequent score
• How is the range of a data set calculated?


  Range is the difference between the maximum and minimum score.
• What is the range of the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  4
• Why might the range not always reflect variability in different distributions?


  Because the range doesn’t change for distributions with different shapes.
• How does distribution A differ from distribution B in terms of spread?


  Distribution B is more spread out and less concentrated than distribution A.
• What is the mean of the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  4
• What does deviation represent in a data set?


  Deviation is the signed distance of a score from the mean.
• How do you calculate the average deviation from the mean?


  By averaging the deviations of each score from the mean.
• What is the average deviation for the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  0
• What is the formula for calculating average squared deviation?


  Average squared deviation is calculated by averaging the squared deviations from the mean.
• What is the average squared deviation for the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  1. 2
• How is sample variance calculated?


  Sample variance is calculated by averaging the squared deviations and dividing by \(N-1\).
• What is the sample variance for the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  1. 33
• Why do we divide by \(N-1\) instead of \(N\) when calculating sample variance?


  To account for the degrees of freedom in the sample.
• What is a variable?


  A variable is something that can vary.
• What is the formula for calculating sample standard deviation?


  Sample standard deviation is the square root of the sample variance.
• What is an example of a categorical variable?

  Handedness
• What is an example of a continuous variable?


  Temperature
• What is the sample standard deviation for the data set {2, 3, 3, 4, 4, 4, 4, 5, 5, 6}?


  1. 15
• What is an example of a discrete variable?


  No. of siblings
• How does the concentration of data affect standard deviation?


  More concentrated data has a smaller standard deviation, while more spread out data has a larger standard deviation.