Study Notes
Measures of central tendency are statistical measures that describe the center of a data set. They include the mean, mode, and median.
- Mean — the average of all data points, calculated by adding all the data and dividing by the number of items. 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 number in a data set when arranged in order. 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 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 range between the first and third quartiles. Example: If Q1 is 10 and Q3 is 20, the interquartile range is 20 - 10 = 10.
Exam Tips
Key Definitions to Remember
- Mean: The average of a data set.
- Mode: The most frequently occurring data point.
- Median: The middle value when data is ordered.
- Range: The difference between the largest and smallest values.
- Percentile: The value below which a given percentage of data falls.
- Quartile: Values dividing data into four equal parts.
- Interquartile Range: The range between the first and third quartiles.
Common Confusions
- Confusing mode with mean or median.
- Forgetting to order data before finding the median.
- Misunderstanding percentiles as percentages.
Typical Exam Questions
- What is the mean of the data set 5, 10, 15, 20, 25? Answer: 15
- What is the mode of the data set 3, 3, 6, 9, 12? Answer: 3
- How do you find the median of an even-numbered data set? Answer: Average the two middle numbers.
What Examiners Usually Test
- Ability to calculate mean, median, and mode.
- Understanding of how to find range and interquartile range.
- Interpretation of percentiles and quartiles in context.