Measures of Central Tendency

Study Notes

Measures of central tendency are statistical tools used to summarize a set of data by identifying the central point within that data set.

• Mean — the sum of all data points divided by the number of data points.
  Example: For the data set 11, 12, 14, 10, 16, the mean is (11 + 12 + 14 + 10 + 16) / 5 = 12.6.
• Mode — the data point that appears most frequently in a data set.
  Example: In the data set 10, 4, 12, 2, 4, 11, 13, 2, 4, the mode is 4.
• Median — the middle value when the data set is ordered from smallest to largest. If there are two middle numbers, the median is their average.
  Example: For the data set 2, 5, 9, 12, 13, 15, 18, 20, 21, 22, 22, 25, 28, the median is 18.
• Percentile — the value below which a certain percentage of data falls.
  Example: If you are the fourth tallest in a group of 20, you are at the 80th percentile.
• Range — the difference between the largest and smallest values in a data set.
  Example: For the data set 11, 7, 11, 18, 5, 6, 4, 16, 23, the range is 23 - 4 = 19.
• Quartile — values that divide a data set into four equal parts.
  Example: The lowest 25% of numbers is the first quartile.
• Interquartile Range — the difference between the upper quartile (Q3) and the lower quartile (Q1).
  Example: If Q1 is 25% and Q3 is 75%, the interquartile range is Q3 - Q1.

Exam Tips

Key Definitions to Remember

• Mean: Sum of observations divided by the number of observations.
• Mode: Most frequently occurring data point.
• Median: Middle value of an ordered data set.
• Percentile: Value below which a percentage of data falls.
• Range: Difference between the largest and smallest values.
• Quartile: Values dividing data into four equal parts.
• Interquartile Range: Difference between the upper and lower quartiles.

Common Confusions

• Confusing median with mean.
• Misidentifying the mode in a data set with no repeating numbers.
• Calculating range without ordering data first.

Typical Exam Questions

• What is the mean of the data set 3, 5, 7, 9, 11? Answer: The mean is 7.
• What is the mode of the data set 2, 4, 4, 6, 8? Answer: The mode is 4.
• How do you find the median of 1, 3, 3, 6, 7, 8, 9? Answer: The median is 6.

What Examiners Usually Test

• Ability to calculate and interpret mean, median, and mode.
• Understanding of how to find percentiles and quartiles.
• Application of range and interquartile range to describe data spread.