Lesson 3: Mean, Median, and Mode

👩🏽‍🏫 Introduction

Ever wondered how we find “average” scores in exams or the “most common” shoe size in your class? 🧠📏 That’s the magic of measures of central tendency: mean, median, and mode!

These tools help us summarize big sets of numbers into one value that represents the center or trend. Whether you’re analyzing test results, salaries, or shoe sizes, these concepts are essential. Let’s explore how each works and when to use them!

• ➕ Calculate the mean (average) of a dataset
• 🔢 Find the median (middle value)
• 🔁 Identify the mode (most frequent value)
• 📊 Apply formulas for grouped data (frequency tables)

🧠 Key Concepts

📌 1. Mean (Ungrouped Data)

• Add all values together, then divide by how many values there are.

Formula:

📌 2. Median (Ungrouped Data)

• Arrange values in ascending order. The median is the middle one.
• If there are two middle numbers, find their average.

📌 3. Mode (Ungrouped Data)

• The number that appears most often in a dataset.
• A set may have one mode, more than one, or none!

📌 4. Median (Grouped Data)

• L = lower boundary of the median class
• n = total frequency
• F = cumulative frequency before median class
• f = frequency of the median class
• h = class width

📌 5. Mode (Grouped Data)

• L = lower boundary of modal class
• f₁ = frequency of modal class
• f₀ = frequency before modal class
• f₂ = frequency after modal class
• h = class width

🔍 Worked Examples

1. 1. Example 1 – Mean (Ungrouped):
      Find the mean of: 4, 7, 6, 3, 5
      ➕ Sum = 25
      
      ✅ Mean = 5

1. 1. Example 2 – Median (Odd Number of Values):
      Find the median of: 6, 2, 9, 4, 5
      🔢 Sorted = 2, 4, 5, 6, 9 → Middle = 5
      ✅ Median = 5

1. 1. Example 3 – Mode (Ungrouped):
      Find the mode of: 3, 6, 3, 2, 4, 3, 6
      🔁 3 appears most (3 times)
      ✅ Mode = 3

1. 1. Example 4 – Median (Even Number of Values):
      Data: 8, 5, 6, 4 → Sorted = 4, 5, 6, 8
      Middle values = 5, 6 →
      
      ✅ Median = 5.5

1. 1. Example 5 – Median (Grouped Data):
      Class Intervals | Frequency
      0–9: 2
      10–19: 6
      20–29: 9 ← Median class
      30–39: 5
      Total n = 22 →
      
      Median class is where cumulative frequency reaches 11 → Class = 20–29
      L = 19.5, F = 8, f = 9, h = 10
      
      ✅ Median ≈ 22.8

1. Example 6 – Mode (Grouped Data):
   Class Intervals | Frequency
   0–9: 4
   10–19: 8 ← Modal class
   20–29: 6
   L = 9.5, f₁ = 8, f₀ = 4, f₂ = 6, h = 10
   
   ✅ Mode ≈ 16.2

✍🏽 Practice Exercises

🅰️ Section A – Ungrouped Data

1. Find the mean of: 10, 12, 8, 6, 14
2. Find the median of: 7, 3, 9, 5, 11
3. Find the mode of: 2, 4, 4, 6, 4, 2, 6

🅱️ Section B – Grouped Data

1. Class Intervals | Frequency
   0–9: 3
   10–19: 7
   20–29: 10
   30–39: 5
   Find the median and mode.

✅ Answers and Explanations

• A1:
  Sum = 50 → Mean =
  
• A2: Sorted = 3, 5, 7, 9, 11 → Median = 7
• A3: 4 appears 3 times → Mode = 4
• B1 (Median): Total = 25 →
  
  Median class = 20–29, L = 19.5, F = 10, f = 10, h = 10
  
• B1 (Mode): Modal class = 20–29
  f₁ = 10, f₀ = 7, f₂ = 5, L = 19.5, h = 10
  

📌 Recap

• ➕ Mean = total ÷ number of values
• 🔢 Median = middle value when sorted
• 🔁 Mode = most frequent value
• 📊 Use grouped data formulas when working with frequency tables

💭 Reflection Prompt

If you recorded your phone screen time over the last 7 days, would the mean or median better represent your daily usage? Why?