📊 Data Presentation: Frequency Distributions

The Story of Sorting Candy 🍬

Imagine you have a huge jar of mixed candies. There are red ones, blue ones, green ones, yellow ones—all jumbled together! You want to know how many of each color you have.

What do you do? You sort them into piles. Red candies here, blue candies there. Then you count each pile.

That’s exactly what frequency distributions do with numbers! They help us take messy, jumbled data and organize it into neat groups so we can understand what we have.

🎯 What You’ll Learn

• Raw Data vs Grouped Data
• Frequency Distribution
• Class Intervals and Boundaries
• Cumulative Frequency
• Relative Frequency
• Constructing Frequency Tables

📦 Raw Data and Grouped Data

Raw Data: The Messy Pile

Raw data is like dumping all your candies on the table without sorting. It’s just a list of numbers—no order, no groups.

Example: Test scores of 10 students:

75, 82, 91, 67, 75, 88, 92, 75, 81, 79

This is raw data. It’s hard to understand at a glance. How many students scored in the 70s? You’d have to count one by one!

Grouped Data: The Sorted Piles

Grouped data is when we put similar numbers together in groups (like sorting candies by color).

Same scores, now grouped:

Now you can instantly see most students scored in the 70s!

💡 Remember: Raw data = messy pile. Grouped data = sorted piles.

🔢 Frequency Distribution

What is Frequency?

Frequency simply means “how many times something happens.”

If you have 3 red candies, the frequency of red is 3.

What is a Frequency Distribution?

A frequency distribution is a table that shows:

• All the different values (or groups of values)
• How many times each one appears

It’s like a scoreboard that tells you the count of each category!

Example: Favorite fruits of 15 kids

Now you know apples win! 🍎

graph TD
    A[Raw Data] --> B[Count Each Value]
    B --> C[Create Table]
    C --> D[Frequency Distribution!]

📏 Class Intervals and Boundaries

Class Intervals: The Boxes

When numbers spread over a big range, we can’t list every single one. Instead, we create boxes called class intervals.

Think of it like sorting books on a shelf:

• Shelf 1: Books with 1-50 pages
• Shelf 2: Books with 51-100 pages
• Shelf 3: Books with 101-150 pages

Each shelf is a class interval!

Example: Ages at a birthday party

Class Width

The class width is how big each box is.

For 5-9: Width = 9 - 5 + 1 = 5 (ages 5, 6, 7, 8, 9)

Class Boundaries: The Invisible Lines

Class boundaries are the exact cutoff points between classes. They prevent gaps!

💡 Why boundaries matter: If someone is exactly 9.5 years old, which group? Boundaries make it crystal clear!

Formula:

• Lower boundary = Lower limit - 0.5
• Upper boundary = Upper limit + 0.5

📈 Cumulative Frequency

Running Total

Cumulative frequency is a running total. It answers: “How many values are at or below this point?”

Think of climbing stairs. At each step, you count all the steps you’ve climbed so far.

Example: Books read by students

Now you can say: “17 students read 9 books or fewer!”

graph TD
    A[Start: 0] --> B[Add 5 → 5]
    B --> C[Add 8 → 13]
    C --> D[Add 4 → 17]
    D --> E[Add 3 → 20]

📊 Relative Frequency

The Percentage Story

Relative frequency tells you the proportion or percentage of each group.

It answers: “What fraction of the total is this?”

Formula:

Relative Frequency = Frequency ÷ Total

Example: Favorite colors of 20 kids

Now you can say: “40% of kids prefer blue!” That’s almost half!

💡 All relative frequencies add up to 1 (or 100% as percentages)

🛠️ Constructing Frequency Tables

Your Step-by-Step Recipe

Building a frequency table is like baking a cake—follow the steps!

Step 1: Look at Your Data

Find the smallest and largest values.

Example data: Heights of 12 plants (in cm)

23, 45, 31, 28, 52, 39, 47, 33, 41, 29, 36, 50

• Smallest: 23
• Largest: 52
• Range: 52 - 23 = 29

Step 2: Decide on Class Intervals

Choose 5-7 classes usually. Make them equal width.

Range ÷ Number of classes = Width 29 ÷ 5 = about 6

Let’s use classes of width 10: 20-29, 30-39, 40-49, 50-59

Step 3: Make Tally Marks

Go through each number and make a mark!

Step 4: Count the Tallies

Step 5: Add Cumulative & Relative Frequency (Optional)

graph TD
    A[1. Find Range] --> B[2. Choose Classes]
    B --> C[3. Tally Each Value]
    C --> D[4. Count Frequencies]
    D --> E[5. Add Extras]
    E --> F[Done! 🎉]

🎯 Quick Summary

🚀 You Did It!

Now you can:

• ✅ Turn messy raw data into organized groups
• ✅ Create frequency distributions like a pro
• ✅ Understand class intervals and boundaries
• ✅ Calculate running totals with cumulative frequency
• ✅ Find percentages with relative frequency
• ✅ Build your own frequency tables from scratch

Data isn’t scary anymore—it’s just candy waiting to be sorted! 🍬📊