Statistics is all about collecting, organising, and understanding data through... Show more
Mathematics15 views·Updated May 22, 2026·3 pagesJunior Certificate Maths Notes: Comprehensive Statistics Guide
K
Kyla McInerney@kylamcinerney
1 / 3
1
of 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!
2
of 3
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.
3
of 3
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.
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Mathematics15 views·Updated May 22, 2026·3 pagesJunior 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.
1
of 3Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
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!
2
of 3Sign up to see the content. It's free!
- Access to all documents
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- 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.
3
of 3Sign up to see the content. It'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.
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What is the Knowunity AI companion?
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You can download the app in the Google Play Store and in the Apple App Store.
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