Lesson 1: Frequency Distribution and Tables

👩🏽‍🏫 Introduction

Have you ever tallied how many times your favorite artist’s song played on the radio, or how often each friend in a group brings snacks to class? 🍬🎶 You’re already thinking like a statistician!

Statistics help us organize and analyze data in meaningful ways. In this lesson, we’ll learn how to arrange data into frequency tables—a foundational skill in data handling. Whether it’s survey responses, test scores, or even the number of steps you take each day 🚶🏽‍♂️, frequency distribution makes it easy to interpret!

• 📊 Understand what raw data and frequency distributions are
• 🧮 Learn to create and read frequency tables
• 📈 Group data into class intervals for easier analysis

🧠 Key Concepts

📌 1. Raw Data and Frequency

• Raw data is unorganized data collected from observations or surveys (e.g., test scores of students).
• Frequency is the number of times a particular value appears in a dataset.

📌 2. Frequency Distribution Table

This is a table that shows how often each value or range of values occurs in a dataset.

For ungrouped data (when individual values are listed):

For grouped data (when data is grouped into ranges):

📌 3. Class Intervals and Class Width

• A class interval groups values into ranges (e.g., 10–19).
• Class width is the difference between the upper and lower boundaries of a class.

For example: Class interval = 10–19 → Class width =
(we add 1 when using whole numbers)

🔍 Worked Examples

1. 1. Example 1 – Creating a Frequency Table (Ungrouped Data):
      The marks out of 10 scored by 8 students are: 3, 5, 3, 6, 5, 7, 6, 3.

      Step 1: List the unique scores in ascending order.
      Step 2: Count how many times each appears.

      Score	Frequency (f)
      3	3
      5	2
      6	2
      7	1

1. 1. Example 2 – Grouping Data into Class Intervals:
      Ages of 12 students: 13, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 21.

      Step 1: Choose suitable intervals (e.g., 13–15, 16–18, 19–21)
      Step 2: Tally the number of students in each interval

      Age Interval	Frequency (f)
      13–15	4
      16–18	5
      19–21	3

1. Example 3 – Determining Class Width:
   Given class interval 10–14
   Class width =
   
   🟢 Answer: Class width = 5

✍🏽 Practice Exercises

🅰️ Section A – Frequency Table

1. List the frequency of each number in the set: 2, 4, 2, 3, 2, 4, 5, 5, 5, 3.

🅱️ Section B – Grouped Data

1. Group the following ages into 3 equal intervals and create a frequency table:
   12, 14, 16, 18, 20, 22, 24, 26, 28

🅾️ Section C – Class Width

1. Find the class width of the interval 30–39.

✅ Answers and Explanations

• A1:
  

  Number	Frequency
  2	3
  3	2
  4	2
  5	3

• B1: Suggested intervals: 12–17, 18–23, 24–29
  

  Age Group	Frequency
  12–17	3
  18–23	3
  24–29	3

• C1:
  
  🟢 Class width = 10

📌 Recap

• 📊 Raw data becomes more useful when we organize it into frequency tables
• 📐 Ungrouped data lists individual values; grouped data uses class intervals
• 🧮 Class width helps define the range of grouped data

💭 Reflection Prompt

Think about something you do regularly—watch movies, eat snacks, or track your workouts. Could you create a frequency table to summarize your habits over a week? How might it help you understand your behavior better? 📅