Pie charts

Habari Mwanafunzi! Let's Talk About Data Pizza!

Ever shared a pizza or a big, round mandazi with your friends? You cut it into slices, right? The bigger the person's appetite, the bigger the slice they get! In a way, you were already doing statistics! Today, we are going to learn about a special kind of chart that works just like that pizza – it's called a Pie Chart.

A pie chart is a powerful way to show information visually. Instead of just looking at a boring table of numbers, a pie chart turns that data into a colourful circle that's easy to understand at a glance. It helps us see the "parts of a whole," just like the slices make up a whole pizza.

Image Suggestion: A vibrant, colourful, and appetising illustration of a large pizza sliced into different-sized pieces. Next to it, a pie chart with matching colours and proportions, labeled with things like "Favourite Subjects: Maths, English, Kiswahili, Science". The style should be fun and cartoonish.

What Exactly is a Pie Chart?

A pie chart is a circular statistical graphic, which is divided into slices (we call them sectors) to illustrate numerical proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents.

• The whole circle represents the total amount of data, which is always 100% or 360 degrees.
• Each "slice" or sector represents a different category or item.
• The size of the slice shows you its proportion – a bigger slice means a bigger value!

      +-----------------+
     /                   \
    /      Maths (40%)    \
   /                       \
  +-------------------------+
  |  Kiswahili (25%) |      |
  |                  | Sci  |
  +------------------+ (15%)|
   \  English (20%) /
    \               /
     +-------------+

(A simple ASCII art representation of a pie chart)

The Main Ingredient: Calculating the Angles

To draw a pie chart accurately, you can't just guess the size of the slices. We need to do some mathematics! We need to convert the data for each category into an angle in degrees. Remember, a full circle has 360 degrees.

The magic formula is:

Angle of a Sector = (Frequency of the item / Total Frequency) * 360°

Let's see this in action with a real Kenyan example.

Scenario: A farmer in Embu surveyed her small shamba to see which cash crops took up the most space. Here is her data:

• Tea: 12 acres
• Coffee: 9 acres
• Macadamia: 6 acres
• Avocado: 3 acres

Let's calculate the angles to represent this on a pie chart!

Step 1: Find the Total Frequency (Total land size).

Total Acres = 12 (Tea) + 9 (Coffee) + 6 (Macadamia) + 3 (Avocado)
Total Acres = 30 acres

Step 2: Calculate the angle for each crop using our formula.

Tea:
(12 / 30) * 360° = 0.4 * 360° = 144°

Coffee:
(9 / 30) * 360° = 0.3 * 360° = 108°

Macadamia:
(6 / 30) * 360° = 0.2 * 360° = 72°

Avocado:
(3 / 30) * 360° = 0.1 * 360° = 36°

Quick Check: A good student always checks their work! The total of all angles should be 360°. Let's see: 144° + 108° + 72° + 36° = 360°. Perfect! We are ready to draw.

Let's Get Practical: Drawing the Pie Chart

Now that we have our angles, it's time to become an artist! You will need your mathematical instruments: a compass, a protractor, a ruler, and a pencil.

1. Draw the Circle: Use your compass to draw a neat, perfect circle. Mark the center point.
2. Draw the First Line (Radius): Use your ruler to draw a straight line from the center of the circle to its edge. This is your starting point.
3. Measure the First Angle: Place your protractor on the center point, with its baseline aligned with the radius you just drew. Measure the first angle (for Tea, it was 144°) and make a small mark.
4. Draw the Second Line: Remove the protractor and use your ruler to draw a line from the center to the 144° mark. You have just drawn your first slice!
5. Repeat for Other Slices: Now, move your protractor. Place its baseline on the new line you just drew. Measure the next angle (108° for Coffee), make a mark, and draw the line. Continue this process for all your categories.
6. Label Everything: Your pie chart is not complete without labels! Clearly write the name of the category (e.g., "Tea") and its value or percentage in each slice. Don't forget to give your chart a clear, descriptive title, like "Distribution of Crops on an Embu Farm".

Image Suggestion: A close-up, top-down photograph of a Kenyan student's hands drawing a pie chart. You can see a compass, a protractor, and a pencil on a piece of graph paper. The chart is partially drawn, showing the student accurately measuring an angle with the protractor. The scene should look like a typical classroom setting.

Reading a Pie Chart: What Does It All Mean?

Drawing is only half the job. You also need to be able to read and understand a pie chart someone else has made. Let's say you are given a pie chart showing a family's monthly budget of Ksh 60,000.

The chart shows that School Fees takes up a sector of 90°. How much money in Shillings is that?

We can work backwards using a similar formula!

Amount = (Angle of Sector / 360°) * Total Amount

Let's calculate it:

Amount for School Fees = (90° / 360°) * Ksh 60,000
Amount for School Fees = (1 / 4) * Ksh 60,000
Amount for School Fees = Ksh 15,000

See? It's that simple! By looking at the chart, you can quickly see which expense is the largest (it will have the biggest slice) and calculate the exact values if you know the total.

Summary and Kazi ya Mwanafunzi (Your Turn!)

Wow, we have learned a lot! We now know:

• A pie chart shows parts of a whole, like slices of a pizza.
• The whole circle is 360° or 100%.
• How to calculate the angle for each sector to draw the chart accurately.
• How to interpret a pie chart to find actual values.

Now, it's your time to practice. Here is a small task for you. A survey was done in your class to find out the favourite sport of 40 students.

Data:

• Football: 20 students
• Athletics: 10 students
• Volleyball: 6 students
• Basketball: 4 students

Your task is to: 1. Calculate the angle for each sport. 2. Draw a neat, well-labelled pie chart to represent this information.

Keep practicing, and soon you will be a master of pie charts! Kazi nzuri!

Habari! Let's Slice Up Some Data with Pie Charts!

Ever shared a mandazi or a cake with your friends? You cut it into slices, right? The bigger the person's appetite, the bigger the slice they get! A pie chart works exactly like that, but instead of sharing a snack, we are sharing information. It's a circular chart sliced into sectors, where each slice shows a piece of a whole. It's one of the most colourful and visual ways to understand data at a glance. By the end of this lesson, you'll be a pro at both creating and understanding them. Tuko pamoja?

Image Suggestion: A vibrant and cheerful cartoon-style illustration of a Kenyan student looking thoughtfully at a giant, colourful pie chart that is shaped like a mandazi. The slices of the 'mandazi' chart are labelled with fun activities like "Homework," "Playing Football," "Helping at Home," and "Watching TV." The background has subtle Kenyan patterns.

Why Use a Pie Chart?

Pie charts are fantastic for showing proportions. They help us see how much each category contributes to the whole. Think about it:

• How a county government spends its budget (e.g., a big slice for Health, a smaller one for Sports).
• The most popular subjects in your class (Mathematics might have the biggest slice!).
• The main sources of electricity in Kenya (a slice for Hydro, a slice for Geothermal, etc.).

The whole circle always represents the total, or 100%. Each slice is a percentage of that total.

Let's Cook: How to Draw a Pie Chart

Drawing a pie chart is a step-by-step process. All you need is your data, a pencil, a compass, and a protractor. Let's use a local example.

Scenario: A farmer in Makueni County harvested 180 bags of produce in one season. The harvest was made up of Maize, Beans, Pigeon Peas, and Sorghum. Here is the data:

• Maize: 90 bags
• Beans: 45 bags
• Pigeon Peas: 30 bags
• Sorghum: 15 bags

Step 1: Find the Total

First, make sure you have the total amount. If it's not given, you must calculate it. In our case, it's easy!

90 (Maize) + 45 (Beans) + 30 (Pigeon Peas) + 15 (Sorghum) = 180 bags

Step 2: Calculate the Angle for Each Slice

A full circle has 360 degrees (360°). To find out how big each slice should be, we need to convert each category's value into an angle. We use this simple formula:

Angle of a slice = (Value of the category / Total Value) * 360°

Let's calculate the angle for each type of produce:

• Maize:

  (90 / 180) * 360° = 0.5 * 360° = 180°

• Beans:

  (45 / 180) * 360° = 0.25 * 360° = 90°

• Pigeon Peas:

  (30 / 180) * 360° = (1/6) * 360° = 60°

• Sorghum:

  (15 / 180) * 360° = (1/12) * 360° = 30°

Quick Check: The angles should always add up to 360°. Let's check: 180° + 90° + 60° + 30° = 360°. Perfect!

Step 3: Draw and Label the Chart!

Now for the fun part. Grab your geometry set!

1. Use a compass to draw a perfect circle.
2. Mark the center and draw a straight line from the center to the edge (this is the radius). This is your starting line.
3. Place your protractor on the center, aligning its baseline with your starting line. Measure the first angle (e.g., 180° for Maize) and mark it. Draw a line from the center to this mark.
4. Now, use this new line as your baseline. Place the protractor on it and measure the next angle (90° for Beans).
5. Continue this process until all your slices are drawn.
6. Label each slice clearly with the category name and its value or percentage. Don't forget to give your pie chart a title!

Image Suggestion: A clean, top-down photograph of a student's desk. On an open mathematics textbook, there is a geometry set neatly arranged: a compass, a protractor, a ruler, and a sharp pencil. The textbook page shows the beginnings of a hand-drawn pie chart. The style should be educational and focused.

Here’s what our farmer's chart would look like in ASCII art:

        Makueni Farmer's Harvest (180 Bags)
              +------------------+
             /                   /
            /     Sorghum (30°)\
           /       (15 bags)    \
          +----------------------+
         / \       Pigeon Peas  /
        /   \      (60°)      /
       /     \   (30 bags)   /
      / Beans \             /
     / (90°)   \-----------+
    / (45 bags)             \
   /                         \
  /         Maize             \
 /         (180°)              \
/        (90 bags)              \
+-------------------------------+

Reading a Pie Chart: Working Backwards

Sometimes, you are given a pie chart and asked to find the actual values. This is just as easy! Let's say a student has a monthly budget of KES 2,000 for their expenses, shown in the pie chart below.

If the slice for "Airtime" has an angle of 54°, how much money is that?

Formula for Finding the Value from an Angle:

Value = (Angle of the slice / 360°) * Total Amount

Calculation:

Amount spent on Airtime = (54° / 360°) * KES 2,000
                       = 0.15 * 2,000
                       = KES 300

See? Simple! The student spends KES 300 on airtime each month.

Pie Charts in the Real World (Kenya Edition)

Have you ever seen the national budget summary on the news? It's often shown as a pie chart! A big slice for "Education", another big one for "Infrastructure" (like building new roads!), and smaller slices for other ministries. This helps citizens quickly understand where the government is planning to spend their tax money. Next time you watch the news with your parents, look out for it!

Image Suggestion: A realistic mock-up of a Kenyan newspaper's front page. The main story has the headline "COUNTY ALLOCATES KES 10 BILLION BUDGET". The centerpiece is a clean, professional pie chart showing budget allocation with clear labels like 'Healthcare (30%)', 'Education (25%)', 'Agriculture (15%)', 'Roads (20%)', and 'Other (10%)'.

Key Takeaways

• A pie chart shows parts of a whole.
• The entire circle is 360° or 100%.
• To draw a slice, you calculate its angle: (Item Value / Total Value) * 360°.
• To find a value from a slice, you calculate: (Angle / 360°) * Total Value.
• Always remember to give your chart a title and label the slices!

Hongera! You have successfully learned the ins and outs of pie charts. They are a powerful tool for telling a story with data. Now, you can look at data and decide if a pie chart is the best way to present it. Sawa?

Habari Mwanafunzi! Let's Talk About Pie Charts!

Have you ever shared a chapati or a cake with your friends? You cut it into slices, right? The biggest person might get the biggest slice, and so on. In mathematics, we have something very similar, and it’s called a Pie Chart. It’s a super useful and visual way to see how a whole thing is shared or divided. Today, we are going to become masters of pie charts. Tuanze safari!

Imagine your school's sports day. The final points for each house are in: Simba House got 100 points, Chui House got 75, Twiga House got 50, and Nyati House got 25. How can we quickly show who was the champion and how the other houses performed? A pie chart is the perfect tool!

What Exactly is a Pie Chart?

A pie chart is a circular graph that is divided into slices (we call them sectors) to show numerical proportion. The entire circle represents the total amount (or 100%), and the size of each slice shows its part of the total. It’s called a pie chart because it looks like a pie that has been sliced up!

The key ingredients you need are:

• The Circle: This is our "whole pie" or "chapati". It represents the total value of all your data combined. In terms of angles, a full circle is always 360 degrees (360°).
• The Sectors (Slices): Each slice represents a different category. The bigger the slice, the larger the value it represents.
• The Title: It tells everyone what the pie chart is all about (e.g., "Favorite Subjects in Form 2").
• The Key (or Legend): This is a small box that explains what the different colours or patterns in the slices mean.

Image Suggestion: A vibrant, colourful illustration of a pie chart next to an actual sliced cake. The pie chart has 4 slices labeled 'Maths', 'English', 'Science', 'Swahili'. The cake is also cut into 4 unequal slices. A friendly cartoon teacher is pointing from the cake to the chart, with the text "They work the same way!" in a speech bubble.

How to Create a Pie Chart: From Data to Diagram

This is where the magic happens! Let's learn how to take raw numbers and turn them into a beautiful, informative pie chart. We will use a classic Kenyan example.

Scenario: A survey was done among 60 students in a Nairobi school to find out how they travel to school.

• Matatu: 30 students
• Walking: 15 students
• School Bus: 10 students
• Bodaboda: 5 students

Follow these steps carefully. They are your recipe for a perfect pie chart!

Step 1: Find the Total

First, add up all the values to get the total. This is our "whole pie".

Total Students = 30 (Matatu) + 15 (Walking) + 10 (School Bus) + 5 (Bodaboda)
Total Students = 60

Step 2: Calculate the Angle for Each Slice

Remember, a full circle has 360°. To find the size of each slice (sector), we use a simple formula. We first find the fraction of the total for each category and then multiply by 360°.

Formula: Angle of a Sector = (Value of the Category / Total Value) * 360°

Let's calculate the angle for each mode of transport:

Matatu:
(30 / 60) * 360°
= 0.5 * 360°
= 180°

Walking:
(15 / 60) * 360°
= 0.25 * 360°
= 90°

School Bus:
(10 / 60) * 360°
= (1/6) * 360°
= 60°

Bodaboda:
(5 / 60) * 360°
= (1/12) * 360°
= 30°

Quick Check: All your angles should add up to 360°. Let's see: 180° + 90° + 60° + 30° = 360°. Perfect! Our math is correct.

Step 3: Draw and Label the Chart

Now, grab your geometry set!

1. Use a compass to draw a perfect circle.
2. Mark the center and draw a radius (a line from the center to the edge). This is your starting line.
3. Place your protractor on the center, with its baseline on your starting line.
4. Measure the first angle (e.g., 180° for Matatu) and draw the line for that sector.
5. From this new line, measure the next angle (90° for Walking), and so on, until all sectors are drawn.
6. Label each sector clearly with its category and you can also add the percentage or the value. Colour each sector differently!
7. Don't forget the Title and a Key!

Here is a simple ASCII art representation of our finished pie chart:

      Travel to School for 60 Students
        +----------------------------+
       /              |              \
      /   Matatu      |      Bus      \
     /    (180°)      |     (60°)      \
    /                 |------+---------\
   /                  | Boda | Walking  \
  |                   | (30°)|  (90°)   |
  |                   +------+----------|
  |                                     |
   \                                   /
    \                                 /
     \                               /
      \                             /
       \___________________________/

Key:
- Matatu
- Walking
- School Bus
- Bodaboda

Image Suggestion: A clean and colourful pie chart based on the "Travel to School" data. Each sector has a distinct colour (e.g., yellow for Matatu, green for Walking, blue for School Bus, red for Bodaboda). A legend/key is clearly visible on the side. The title "How Students Travel to School in Nairobi" is at the top.

Reading and Interpreting Pie Charts

Sometimes, you are given a pie chart and asked to get information from it. This is like being a detective! Let's look at another example.

Scenario: A farmer in Kericho has a shamba (farm) of 200 acres. The pie chart below shows how the land is used for different crops. The chart shows: Tea (50%), Maize (25%), Sugarcane (15%), and Vegetables (10%).

Question 1: Which crop uses the most land?

Answer: Easy! Just look for the biggest slice. In this case, it's Tea with 50%.

Question 2: How many acres are used for growing Maize?

Answer: Now we need to do a small calculation. We find the percentage of the total area.

Area for Maize = (Percentage for Maize / 100) * Total Area
Area for Maize = (25 / 100) * 200 acres
Area for Maize = 0.25 * 200
Area for Maize = 50 acres

So, the farmer uses 50 acres for growing maize. Sawa?

When Should You Use a Pie Chart?

Pie charts are fantastic, but they are not always the best choice. Here's a quick guide:

• Use a pie chart when: You want to show parts of a whole. It works best with a small number of categories (usually less than 7). For example, showing the different tribes in your class.
• Do NOT use a pie chart when: You want to show changes over time (use a line graph for that!) or when you have too many categories (it will look like a mess - use a bar chart instead!).

Cheza na Nambari (Play with Numbers!)

It's your turn! Try this on your own. In a class of 40 students, 20 said their favourite artist is Nyashinski, 10 chose Sauti Sol, 5 chose Khaligraph Jones, and 5 chose Femi One.

1. Find the angle for each artist's sector.
2. Try to sketch the pie chart.

You can do it! Remember the steps. Practice is the key to becoming a Mathematics champion.

Hongera! You have now learned the essentials of pie charts. Keep practicing, and soon you'll be able to read and create them with ease.