Fix the mistake: Distribution of Data

Data Distributions ① Frequency Distribution Tables

We create a frequency distribution table to organize data. Divide the range of the data into intervals of equal width called classes, and count the number of data values in each class, called the frequency.

Terminology

  • Class: An interval into which data are divided (example: 10 or more and less than 20)
  • Class width: The size of each interval (example: 10)
  • Frequency: The number of data values in each class
  • Class mark: The middle value of each class (example: 10 or more and less than 20 → 15)
📘 Example ①
Organize the test scores 55, 62, 70, 45, 80, 73, 58, 66, 91, 77 into a frequency distribution table (40 or more and less than 100, class width 10).
Answer:
40-50: 1 (45) / 50-60: 2 (55,58) / 60-70: 2 (62,66) / 70-80: 3 (70,73,77) / 80-90: 1 (80) / 90-100: 1 (91)
💡 Key Point
  • Divide classes into “or more to less than” intervals (a boundary value is not included in the upper class)
  • Class mark = (lower limit + upper limit) / 2
  • Total frequency = number of data values

Practice Problems

  1. Organize the data 12, 8, 15, 22, 9, 18, 25, 14, 20, 7 into a frequency distribution table using “5 or more and less than 25, class width 5.”

Answer and Explanation

  1. Answer: 5-10: 3 (8,9,7) / 10-15: 3 (12,14,12) → Actually (12,15,14) / 15-20: 2 (18,15) → Organized: 5-10:3(7,8,9), 10-15:3(12,14,15 ※15 belongs to 15 or more and less than 20), 15-20:3(18,15 belongs to the previous class), 20-25:2(22,20,25)... Recheck the data: 5 or more and less than 10: 7,8,9→3 values, 10 or more and less than 15: 12,14→2 values, 15 or more and less than 20: 15,18→2 values, 20 or more and less than 25: 22,20→2 values, 25 or more and less than 30: 25→1 value.

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