Pie charts

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

Ever shared a pizza or a big, round chapati with your friends? You try to make sure everyone gets a fair slice, right? Some slices might be big, some might be small, but all the slices together make one whole chapati. That's exactly how a pie chart works! It's a fun, circular graph that shows us how a whole thing is divided into different parts. Today, we are going to become masters of slicing and dicing data into beautiful, easy-to-understand pie charts. Twende kazi!

Image Suggestion: A vibrant, colourful illustration of a group of diverse Kenyan students in school uniform, happily sharing a large circular chapati that is cut into unequal slices. The scene is bright and cheerful, set in a school compound with acacia trees in the background.

What Exactly is a Pie Chart?

A pie chart is a type of graph in which a circle is divided into sectors (the "slices"). Each sector represents a part of a whole set of data. The bigger the slice, the more it represents. It's perfect for showing proportions and percentages at a glance.

Imagine you ask 100 students at your school what their favourite local fruit is. You could show your results like this:

• Mangoes: 50 students
• Bananas: 25 students
• Oranges: 15 students
• Avocadoes: 10 students

A pie chart would instantly show you that mangoes are the big favourite (it would be the biggest slice!) and that avocados are the least favourite among the choices. It's a picture of your data!

The Secret Ingredient: Calculating the Angles

Now, how do we know how big to make each slice? We can't just guess! In mathematics, we use angles. A full circle has 360 degrees (360°). This is our "whole chapati." The total of all your data is equal to this 360°.

To find the angle for each slice (or sector), we use a simple formula:

Angle of a sector = (Value of the item / Total value of all items) * 360°

Don't worry, it's easier than it looks. Let's try it with an example!

Let's Make Our Own Pie Chart: A Farmer's Livestock

Let's say a farmer in Nakuru County, Mama Boke, has 60 animals on her shamba. Let's break it down and draw a pie chart to represent her livestock.

Step 1: List the Data

• Cows (Ng'ombe): 10
• Goats (Mbuzi): 25
• Chickens (Kuku): 20
• Sheep (Kondoo): 5

Step 2: Find the Total

First, we add up all the animals to confirm our total.

Total animals = 10 + 25 + 20 + 5 = 60 animals

Excellent! Our total is 60. This "60" represents our whole circle, the 360°.

Step 3: Calculate the Angle for Each Animal

Now we use our magic formula for each group of animals.

• Cows:

  (10 / 60) * 360° = 60°

• Goats:

  (25 / 60) * 360° = 150°

• Chickens:

  (20 / 60) * 360° = 120°

• Sheep:

  (5 / 60) * 360° = 30°

Quick Check: A good way to know you are correct is to add up all your angles. They should equal 360°.
60° + 150° + 120° + 30° = 360°. Perfect!

Step 4: Draw and Label the Chart

Now you would take a compass to draw a perfect circle. Then, using a protractor, you measure and draw each angle. Start with a straight line from the center to the edge, then measure your first angle (e.g., 60° for Cows) and draw the next line. From that new line, measure the next angle (150° for Goats), and so on, until all your slices are drawn.

Finally, label each slice and give your chart a title!

    Mama Boke's Livestock (60 Animals)
           +------------------+
        ,'                    `.
      ,'       Goats (150°)     `.
     /                            \
    /      (The biggest slice)     \
   /                                \
  ,'                                 `.
 /                                    \
 |  Chickens                          |
 |  (120°)                             |
 |                .Cows(60°)           |
 \                 `----------,       /
  `._ Sheep(30°)           ,'       ,'
     `._                  ,'      ,'
        `._              ,'     ,'
           `+----------+'

Just by looking, you can immediately see that Mama Boke has more goats than any other animal!

Reading the Story: How to Interpret a Pie Chart

Pie charts tell a story without using many words. Let's imagine the student council used KES 100,000 to fund different clubs. They present the spending in a pie chart.

Image Suggestion: A clean, modern, and colourful pie chart titled "Student Council Club Funding (KES 100,000)". The sectors are clearly labelled: Sports Club (45%), Science Club (25%), Drama Club (20%), and Environment Club (10%). Each sector has a small, simple icon like a football, a beaker, drama masks, and a leaf.

By looking at this chart, you could answer questions like:

• Which club received the most funding?
  The Sports Club, because it has the largest slice (45%).
• How much money did the Drama Club receive?
  The chart shows 20%. So, 20% of KES 100,000 is KES 20,000.
• Which two clubs together received half of the total funds?
  You look for slices that add up to 50%. The Science Club (25%) and the Drama Club (20%) and the Environment Club (10%) don't quite make 50%. But let's re-check. Ah, the Science Club (25%) combined with another 25% would work. Let's see... no combination makes exactly 50%. But the Sports Club (45%) and Environment Club (10%) together make 55%, which is more than half! This is the kind of analysis you can do.

Key Takeaways - Your Recipe for Success!

• A pie chart shows parts of a whole in a circular format.
• The entire circle is always 360°.
• The most important formula is: Angle = (Part / Whole) * 360°.
• Always give your pie chart a clear title and label each sector.
• They are excellent for a quick, visual comparison of data.

Challenge Yourself!

Your class teacher conducted a survey on 40 students to find out their favourite subject. The results were:
- Mathematics: 12 students
- Kiswahili: 10 students
- English: 8 students
- Science: 6 students
- Social Studies: 4 students

Your Task: Calculate the angle for each subject and imagine how you would draw the pie chart. Which subject would have the biggest slice?

You've done an amazing job today! Pie charts are a powerful tool in statistics, and now you have the skills to build and understand them. Keep practicing, and soon you'll be able to tell stories with data anywhere you go. Hongera!

Habari Mwanafunzi! Let's Cut a Slice of Knowledge with Pie Charts!

Have you ever shared a birthday cake or a pizza with your friends? Everyone gets a slice, right? Some slices might be big, some might be small, but all the slices together make up the whole cake. Now, what if I told you that this simple idea of sharing a cake can help us understand and show information in Mathematics? Karibu! Welcome to the lesson on Pie Charts!

A pie chart is just like that cake. It's a special type of circle graph that shows how a whole thing is divided into different parts. It's perfect for showing 'part-to-whole' relationships.

Real-World Example: Imagine your school's prefects are chosen from different houses: Simba, Twiga, Nyati, and Chui. A pie chart could quickly show us what percentage of prefects comes from each house. The whole "pie" would be all the prefects, and each "slice" would be a house.

The Key Ingredients: Understanding the Circle

Before we start "baking" our charts, we need to remember a very important fact about circles:

• A full circle has a total of 360 degrees (360°).
• This 360° represents our 'whole' or 100% of the data we are looking at.
• Each slice, which we call a sector, will have its own angle. The bigger the angle, the bigger the slice!

To calculate the angle for each sector, we use a simple and powerful formula:

Angle of a sector = (Value of the item / Total value of all items) × 360°

Let's Get Practical: A Farmer's Harvest in Makueni

Let's help a farmer from Makueni County to represent his fruit harvest in a pie chart. It will help him see which fruit he harvests the most!

His harvest for the season was:

• Mangoes: 90 kgs
• Oranges: 60 kgs
• Avocados: 45 kgs
• Pawpaws: 45 kgs

Step 1: Find the Total Harvest

First, we must find the total weight of all the fruits. This is our "whole pie".

Total Harvest = 90 (Mangoes) + 60 (Oranges) + 45 (Avocados) + 45 (Pawpaws)
Total Harvest = 240 kgs

Step 2: Calculate the Angle for Each Fruit (Each Sector)

Now, we use our magic formula for each type of fruit.

Mangoes:

Angle for Mangoes = (90 / 240) × 360°
                  = (3 / 8) × 360°
                  = 135°

Oranges:

Angle for Oranges = (60 / 240) × 360°
                  = (1 / 4) × 360°
                  = 90°

Avocados:

Angle for Avocados = (45 / 240) × 360°
                   = (3 / 16) × 360°
                   = 67.5°

Pawpaws:

Angle for Pawpaws = (45 / 240) × 360°
                  = (3 / 16) × 360°
                  = 67.5°

Quick Check: All the angles should add up to 360°. Let's see: 135° + 90° + 67.5° + 67.5° = 360°. Perfect! Our calculations are correct.

Step 3: Draw the Pie Chart

Now you would take a compass to draw a circle, and a protractor to measure and draw each angle. Remember to label each slice clearly!

        +---------------------------------+
       /           Harvest in Makueni      \
      /                 (kgs)               \
     |                                       |
     |         Mangoes (135°)                |
     |      ,""                             |
     |    ,"                                |
     |  ,"                                  |
     +O------------------+ Oranges (90°)     |
     | ` .               |                   |
     |   ` . Avocados    |                   |
     |     ` . (67.5°)   |                   |
      \        ` .       / Pawpaws (67.5°)   /
       \         ` .    /                   /
        +---------------------------------+
          (A simple ASCII art representation)

Image Suggestion: A colourful and clear pie chart titled 'Fruit Harvest in Makueni'. The largest sector, labeled 'Mangoes (135°)', is a vibrant orange colour. The 90° sector for 'Oranges' is bright orange. The two smaller, equal sectors for 'Avocados (67.5°)' and 'Pawpaws (67.5°)' are green and yellow respectively. A small key or legend is visible on the side. The style is educational and clean.

Reading a Pie Chart: Spending Pocket Money

Sometimes, you are given a pie chart and asked to find the actual values. Let's try it. A student in Nairobi is given KSh 1,500 for pocket money per month. The pie chart below shows how they spend it.

Monthly Spending (Total: KSh 1,500)

• Snacks: 40%
• Transport (Matatu fare): 30%
• Airtime: 20%
• Savings: 10%

How much money (in shillings) is spent on Snacks?

Amount for Snacks = (Percentage for Snacks / 100) × Total Amount
                  = (40 / 100) × 1,500
                  = 0.4 × 1,500
                  = KSh 600

See? Easy! You can now calculate the amount for transport, airtime, and savings using the same method.

When to Use (and Not Use) a Pie Chart

Pie charts are fantastic, but they are not always the best tool for the job.

• Great for: Showing percentages and how a single group is broken down. For example, the different tribes in your class.
• Not so great for: Comparing different groups or showing changes over time. If you wanted to compare the farmer's harvest this year to last year, a Bar Chart would be a better choice. It's also hard to read if you have too many small slices!

Mazoezi Time (Your Turn!)

You are now on your way to becoming a pie chart expert! Try this challenge:

In a class of 40 students, 20 said their favourite sport is Football, 10 chose Volleyball, and 10 chose Basketball. Calculate the angle for each sector (Football, Volleyball, and Basketball) that you would use to draw a pie chart of this data.

Keep practicing, and soon you'll be able to read and create pie charts with confidence. Kazi nzuri!

Habari Mwanafunzi! Let's Talk About Maths Pizza!

Have you ever shared a pizza or a birthday cake with your friends? You cut it into slices, right? The bigger the person's appetite, the bigger the slice they might get! A pie chart works in exactly the same way. It's like a "maths pizza" that helps us see how a whole thing is shared or divided into different parts. It's a powerful and visual way to understand information at a single glance. By the end of this lesson, you'll be able to create and understand these charts like a pro!

Imagine the 47 counties of Kenya. A pie chart could show how the total population is distributed among them, with Nairobi getting a large slice and a county like Lamu getting a much smaller one. It immediately shows you where most people live!

What Exactly is a Pie Chart?

A pie chart is a circular graph used in statistics. The entire circle represents the total amount of something, which we call the 'whole'. This 'whole' is then divided into slices, which in mathematics we call sectors. Each sector represents a specific category or part of that whole. The size of the slice (or sector) tells you how big that category is compared to the others.

The entire circle always represents:

• 100% if we are talking in percentages.
• 360 degrees (360°) if we are talking about angles. This is the most important number to remember for our calculations!

Image Suggestion: A vibrant, colourful pie chart on a clean white background. The chart is divided into 4 differently coloured slices (e.g., green, blue, yellow, red). Each slice is slightly pulled out from the center for emphasis. Next to the chart is a clear legend explaining what each colour represents, like 'Maize', 'Beans', 'Sorghum', 'Millet'. The style should be a clear, educational graphic.

From Data to Diagram: Let's Bake Our Pie Chart!

This is where the real fun begins! We are going to take some raw data and turn it into a beautiful, informative pie chart. Let's follow the recipe step-by-step.

Scenario: A survey was done at "Jitegemee Secondary School" to find out the favourite sport of 120 Form 2 students. The results were:

• Football: 60 students
• Volleyball: 30 students
• Athletics: 20 students
• Basketball: 10 students

Step 1: Find the Total

First, we need to know the total number of students surveyed. We can add them up: 60 + 30 + 20 + 10 = 120 students. The problem already gave us this, but it's always good to check!

Step 2: Calculate the Angle for Each Sport

This is the most crucial step. We need to find out how big a slice of our 360° circle each sport gets. We use a simple formula:

Angle of Sector = (Number in Category / Total Number) * 360°

Let's calculate it for each sport:

Football:
(60 / 120) * 360°
= (1/2) * 360°
= 180°

Volleyball:
(30 / 120) * 360°
= (1/4) * 360°
= 90°

Athletics:
(20 / 120) * 360°
= (1/6) * 360°
= 60°

Basketball:
(10 / 120) * 360°
= (1/12) * 360°
= 30°

Quick Check: A correct pie chart's angles must add up to 360°. Let's see: 180° + 90° + 60° + 30° = 360°. Perfect! Our calculations are correct.

Step 3: Draw and Label the Chart

Now you would take a compass to draw a perfect circle. Use a protractor to measure and draw each angle. Start with a line from the center to the edge, measure the first angle (e.g., 180° for Football), draw the line, and then measure the next angle from where the last one ended. Finally, colour each sector differently and add a key or legend so people know what each colour means!

      +---------------------------------+
      |    Favourite Sports at          |
      |   Jitegemee Secondary School    |
      +---------------------------------+
                 , - ~ ~ ~ - ,
             , '               ' ,
           ,                       ,
          ,                         ,
         ,           Football       ,
         ,           (180°)         ,
         ,                          ,
         +--------------------------+
         , Basketball (30°)         ,
         , . . . . . . .            ,
          '. Athletics (60°).     ,'
           ' ,_ _ _ _ _ _ Volleyball,'
             ' , _ (90°) _ , '
                 ' - , _ , - '

  Key:
  [#########] Football
  [.........] Athletics
  [_________] Volleyball
  [         ] Basketball

Reading the Pie Chart: What's the Story?

The power of a pie chart is in its ability to tell a story quickly. Looking at the chart above, you can immediately tell that:

• Football is by far the most popular sport, taking up half the chart!
• Volleyball is the second most popular.
• Very few students chose Basketball compared to Football.

Sometimes, a question might ask you to find the percentage. The formula is just as easy:

Percentage = (Number in Category / Total Number) * 100%

For example, what percentage of students chose Athletics?

Percentage for Athletics = (20 / 120) * 100%
                         = (1/6) * 100%
                         = 16.67%

When is a Pie Chart the Best Choice?

Pie charts are fantastic, but they are not always the best tool for the job. Think of it like this: you wouldn't use a hammer to cut a piece of wood!

Use a pie chart when:

• You are comparing parts of a whole.
• The data adds up to a meaningful total (like 100%).
• You have a small number of categories (usually less than 7). Too many slices make the "pizza" look messy and hard to read!

Avoid a pie chart when:

• You need to show how things change over time (a line graph is better for that).
• The categories do not add up to a whole.

You're Now a Pie Chart Pro!

Congratulations! You've learned the secret recipe for making and understanding pie charts. Just remember the key formula for finding the angle, and you'll be able to turn any set of data into a clear and colourful story.

Remember, the whole point of statistics is to make sense of the world around us. Whether it's tracking the family budget, understanding election results, or showing the crops grown in your county, pie charts are an excellent tool. Keep practicing, and you'll master it in no time. Kazi nzuri!