descriptive statistics

• What is the purpose of descriptive statistics?

  To summarize and describe features of quantitative data
• What are the two main types of descriptive statistics?

  Measures of central tendency and measures of dispersion
• What are the three measures of central tendency?

  Mean, median, and mode
• Why is the mode particularly useful for discrete numbers?

  It isn't affected by outliers and makes sense for categories
• Given the data set: 10,000, 15,000, 15,000, 15,000, 20,000, 24,000, 24,000, 26,000, 36,000, 195,000, what is the mode?


  15,000
• What is a criticism of the mode in small data sets?

  There may be multiple modes or no mode
• Given the data set: 10,000, 15,000, 15,000, 15,000, 20,000, 24,000, 24,000, 26,000, 36,000, 195,000, what is the median?

  22,000
• What is a positive aspect of the median?

  It is not affected by extreme outlier scores
• Given the data set: 10,000, 15,000, 15,000, 15,000, 20,000, 24,000, 24,000, 26,000, 36,000, 195,000, what is the mean?

  38,000
• What is a criticism of the mean?

  It is easily shifted by extreme values
• What are the two main measures of dispersion?

  Range and standard deviation
• Given the data set: 10,000, 15,000, 15,000, 15,000, 20,000, 24,000, 24,000, 26,000, 36,000, 195,000, what is the range?

  185,000
• What is a criticism of the range?

  Extreme scores easily distort its value
• What does a larger standard deviation indicate about a data set?

  The scores are more spread out
• If Group 1 has a standard deviation of 5 and Group 2 has a standard deviation of 10, which group has more consistent scores?

  Group 1
• If 595 out of 2,480 students are studying A-levels, what percentage of students are studying A-levels?

  24%
• If a sample size is 250 and 24% are A-level students, how many A-level students should be included in the sample?

  60
• If the number of A-level students increased from 595 to 724, what is the percentage change?

  21.7%
• What does a negative percentage change indicate?

  A decrease in the number
• What are the three types of correlations?

  Positive, negative, and zero
• What does a correlation coefficient indicate?

  The strength and direction of a relationship
• What are the strengths and weaknesses of the mode?

  Strengths:

  • Not affected by outliers
  • Useful for discrete numbers and categories

  
  

  Weaknesses:

  • In small data sets, there may be multiple modes or no mode
  • Does not include all values in its calculation
• What are the strengths and weaknesses of the median?

  Strengths:

  • Not affected by extreme outlier scores
  • Easy to calculate

  
  

  Weaknesses:

  • Does not include all raw scores in its calculation
  • Less sensitive than the mean
• What are the strengths and weaknesses of the mean?

  Strengths:

  • Includes all raw data in its calculation
  • Sensitive measure of central tendency

  
  

  Weaknesses:

  • Easily shifted by extreme values
• What are the strengths and weaknesses of the range?

  Strengths:

  • Easy to calculate

  
  

  Weaknesses:

  • Easily distorted by extreme scores
  • Does not show how scores are spread out around the mean
• What are the strengths and weaknesses of the standard deviation?

  Strengths:

  • Includes all values in its calculation
  • Shows how spread out or clustered scores are around the mean

  
  

  Weaknesses:

  • Distorted by extreme values
  • More difficult to calculate than the range
• What are the steps to calculate a percentage?

  1. Write the fraction (part/whole)
  2. Convert the fraction to a decimal by dividing
  3. Multiply the decimal by 100 to get the percentage
• What are the steps to calculate a percentage change?

  1. Subtract the old number from the new number
  2. Divide the result by the old number
  3. Multiply by 100 to get the percentage change
• What are the types of correlations and their meanings?

  • Positive correlation: As one variable increases, the other increases
  • Negative correlation: As one variable increases, the other decreases
  • Zero correlation: No relationship between variables