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Updated Apr 18, 2026
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Junior Certificate Maths Notes: Comprehensive Statistics Guide
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Kyla McInerney
@kylamcinerney
1 / 3
Types of Graphs and Charts
Ever wondered how to turn boring numbers into clear, visual information? Bar charts are perfect for showing different categories like favourite hobbies or sports. They use evenly-spaced rectangles with gaps between them and work brilliantly for both ordinal data (things in order) and nominal data (things with no particular order).
Line plots are your go-to choice when you want to show discrete numerical data using dots or crosses along a horizontal line. They're simple but really effective for spotting patterns quickly.
Histograms are the tricky cousins of bar charts - they look similar but have no gaps between bars and can only be used for continuous numerical data. Think of them as showing ranges of numbers rather than separate categories.
Quick Tip: Remember, histograms have NO gaps, bar charts DO have gaps!
For showing parts of a whole, pie charts use a full 360° circle. You'll need to convert your frequency data into degrees using a compass and protractor. Stem and leaf plots are brilliant for organising discrete numerical data - just remember to include every number (even repeats), arrange from smallest to biggest, and always include a key!
Measures of Central Tendency
Finding the "typical" value in a set of data is easier than you think! The mean (or average) is calculated by adding all values together and dividing by how many numbers you have. For example, with the numbers 12, 13, 9, 8, 6, 9, 12, you'd get (12+13+9+8+6+9+12) ÷ 7 = 9.86, which rounds to 10.
The mode is simply the number that appears most often in your data set. It's the easiest one to find - just look for repeats! Some data sets might have more than one mode or no mode at all.
The median is the middle number, but here's the catch - you must arrange your data in order first. With an odd number of values, pick the middle one. With an even number, find the mean of the two middle numbers.
Memory Trick: Mode = Most often, Median = Middle, Mean = Mathematical average!
The range shows how spread out your data is by subtracting the smallest number from the biggest number. It's a quick way to see if your values are close together or widely scattered.
Mean from Frequency Tables
Calculating the mean from a frequency table requires a slightly different approach, but you've got this! Instead of adding individual numbers, you multiply each value by its frequency, add all these products together, then divide by the total frequency.
For a simple frequency table, like ages 10, 15, 20, 25, 30 with frequencies 7, 2, 9, 5, 8, you'd calculate: (10×7 + 15×2 + 20×9 + 25×5 + 30×8) ÷ (7+2+9+5+8) = 645 ÷ 31 = 20.81.
Grouped frequency tables with intervals need an extra step - you must find the mid-interval value (m.i.v.) first. For the interval 0-10, the mid-point is 5; for 10-20, it's 15, and so on. Then use these mid-points in your calculation just like regular values.
Pro Tip: Always double-check your total frequency in the denominator - it's the most common place to make mistakes!
The process stays the same: multiply each mid-interval value by its frequency, add everything up, then divide by the total frequency. This gives you a good estimate of the mean for grouped data.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
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4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Junior Certificate Maths Notes: Comprehensive Statistics Guide
K
Kyla McInerney
@kylamcinerney
Statistics is all about collecting, organising, and understanding data through graphs and calculations. You'll learn how to display information using different types of charts and how to find important values like averages and middle numbers.
Types of Graphs and Charts
Ever wondered how to turn boring numbers into clear, visual information? Bar charts are perfect for showing different categories like favourite hobbies or sports. They use evenly-spaced rectangles with gaps between them and work brilliantly for both ordinal data (things in order) and nominal data (things with no particular order).
Line plots are your go-to choice when you want to show discrete numerical data using dots or crosses along a horizontal line. They're simple but really effective for spotting patterns quickly.
Histograms are the tricky cousins of bar charts - they look similar but have no gaps between bars and can only be used for continuous numerical data. Think of them as showing ranges of numbers rather than separate categories.
Quick Tip: Remember, histograms have NO gaps, bar charts DO have gaps!
For showing parts of a whole, pie charts use a full 360° circle. You'll need to convert your frequency data into degrees using a compass and protractor. Stem and leaf plots are brilliant for organising discrete numerical data - just remember to include every number (even repeats), arrange from smallest to biggest, and always include a key!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Measures of Central Tendency
Finding the "typical" value in a set of data is easier than you think! The mean (or average) is calculated by adding all values together and dividing by how many numbers you have. For example, with the numbers 12, 13, 9, 8, 6, 9, 12, you'd get (12+13+9+8+6+9+12) ÷ 7 = 9.86, which rounds to 10.
The mode is simply the number that appears most often in your data set. It's the easiest one to find - just look for repeats! Some data sets might have more than one mode or no mode at all.
The median is the middle number, but here's the catch - you must arrange your data in order first. With an odd number of values, pick the middle one. With an even number, find the mean of the two middle numbers.
Memory Trick: Mode = Most often, Median = Middle, Mean = Mathematical average!
The range shows how spread out your data is by subtracting the smallest number from the biggest number. It's a quick way to see if your values are close together or widely scattered.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Mean from Frequency Tables
Calculating the mean from a frequency table requires a slightly different approach, but you've got this! Instead of adding individual numbers, you multiply each value by its frequency, add all these products together, then divide by the total frequency.
For a simple frequency table, like ages 10, 15, 20, 25, 30 with frequencies 7, 2, 9, 5, 8, you'd calculate: (10×7 + 15×2 + 20×9 + 25×5 + 30×8) ÷ (7+2+9+5+8) = 645 ÷ 31 = 20.81.
Grouped frequency tables with intervals need an extra step - you must find the mid-interval value (m.i.v.) first. For the interval 0-10, the mid-point is 5; for 10-20, it's 15, and so on. Then use these mid-points in your calculation just like regular values.
Pro Tip: Always double-check your total frequency in the denominator - it's the most common place to make mistakes!
The process stays the same: multiply each mid-interval value by its frequency, add everything up, then divide by the total frequency. This gives you a good estimate of the mean for grouped data.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Mathematics
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Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user