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Updated Mar 22, 2026

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4 pages

Easy Math Notes: Variance and Standard Deviation

user profile picture

Lucía

@luttior

A comprehensive guide to variance and standard deviation in study... Show more

Page 1
Page 2
Page 3
Page 4
1 / 4
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Page 2: Advanced Statistical Applications

This page expands on statistical concepts through practical examples involving pocket money analysis and combined dataset calculations.

Example: Analysis of pocket money distribution among students, with calculations for both mean (£10.22) and standard deviation.

Vocabulary: Standard deviation in this context represents the typical variation in pocket money amounts from the mean value.

The page includes comprehensive calculations for:

  • Combined datasets with different sample sizes
  • Frequency distribution tables
  • Mean and standard deviation calculations using grouped data
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Page 3: Real-World Applications

This section focuses on practical applications of mean standard deviation calculation in exercises through attendance records and machine part lifetime analysis.

Highlight: The analysis of student absences demonstrates how standard deviation can be used to understand variation in attendance patterns.

Example: Machine part lifetime analysis showing:

  • Data grouped into time intervals
  • Frequency distribution analysis
  • Mean lifetime calculation of 16.1 hours
  • Standard deviation of 4.69 hours

The calculations demonstrate practical applications in:

  • Quality control analysis
  • Performance monitoring
  • Statistical inference
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Page 4: Advanced Statistical Analysis

This final page covers advanced applications of statistical concepts through wind speed analysis and probability calculations.

Definition: Daily mean windspeed calculations demonstrate how standard deviation can be used in meteorological analysis.

Example: June 2015 wind speed analysis:

  • Mean: 8.1 knots
  • Standard deviation: 3.41 knots
  • Range: 4-17 knots

The page concludes with important considerations about:

  • Data distribution assumptions
  • Practical applications of standard deviation in real-world scenarios
  • Statistical estimation techniques
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Page 1: Introduction to Basic Statistical Calculations

This page introduces fundamental statistical calculations through practical examples including calculating standard deviation of student height and dog weights.

The page walks through several key calculations:

Example: For a dataset where Σx=24 and Σx²=78 with n=8, the mean is calculated as 3 and variance as 0.75.

Definition: Variance (σ²) represents the average squared deviation from the mean, while standard deviation is the square root of variance.

Highlight: The page demonstrates practical applications through real-world examples including measuring collie dogs' weights and student heights.

A detailed analysis of eight students' heights provides a practical demonstration of statistical concepts:

  • Heights ranging from 165cm to 190cm
  • Mean calculation: 178.125cm
  • Variance calculation: 59.859375 cm²


We thought you’d never ask...

What is the Knowunity AI companion?

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

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Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

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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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

 

Maths

•

192

•

Updated Mar 22, 2026

•

4 pages

Easy Math Notes: Variance and Standard Deviation

user profile picture

Lucía

@luttior

A comprehensive guide to variance and standard deviation in study notes covering various statistical calculations and real-world applications.

  • Detailed exploration of standard deviation calculations across different datasets including student heights, dog weights, and weather patterns
  • Multiple worked examples demonstrating practical... Show more

Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Page 2: Advanced Statistical Applications

This page expands on statistical concepts through practical examples involving pocket money analysis and combined dataset calculations.

Example: Analysis of pocket money distribution among students, with calculations for both mean (£10.22) and standard deviation.

Vocabulary: Standard deviation in this context represents the typical variation in pocket money amounts from the mean value.

The page includes comprehensive calculations for:

  • Combined datasets with different sample sizes
  • Frequency distribution tables
  • Mean and standard deviation calculations using grouped data
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Page 3: Real-World Applications

This section focuses on practical applications of mean standard deviation calculation in exercises through attendance records and machine part lifetime analysis.

Highlight: The analysis of student absences demonstrates how standard deviation can be used to understand variation in attendance patterns.

Example: Machine part lifetime analysis showing:

  • Data grouped into time intervals
  • Frequency distribution analysis
  • Mean lifetime calculation of 16.1 hours
  • Standard deviation of 4.69 hours

The calculations demonstrate practical applications in:

  • Quality control analysis
  • Performance monitoring
  • Statistical inference
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Page 4: Advanced Statistical Analysis

This final page covers advanced applications of statistical concepts through wind speed analysis and probability calculations.

Definition: Daily mean windspeed calculations demonstrate how standard deviation can be used in meteorological analysis.

Example: June 2015 wind speed analysis:

  • Mean: 8.1 knots
  • Standard deviation: 3.41 knots
  • Range: 4-17 knots

The page concludes with important considerations about:

  • Data distribution assumptions
  • Practical applications of standard deviation in real-world scenarios
  • Statistical estimation techniques
Lucia Tormo # variance and standard deviation 4.) Exercise 2E (page 32) 27/01/2023 Q1. Given that for a variable x: $\sum x=24$ $\sum x^2=78

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

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Page 1: Introduction to Basic Statistical Calculations

This page introduces fundamental statistical calculations through practical examples including calculating standard deviation of student height and dog weights.

The page walks through several key calculations:

Example: For a dataset where Σx=24 and Σx²=78 with n=8, the mean is calculated as 3 and variance as 0.75.

Definition: Variance (σ²) represents the average squared deviation from the mean, while standard deviation is the square root of variance.

Highlight: The page demonstrates practical applications through real-world examples including measuring collie dogs' weights and student heights.

A detailed analysis of eight students' heights provides a practical demonstration of statistical concepts:

  • Heights ranging from 165cm to 190cm
  • Mean calculation: 178.125cm
  • Variance calculation: 59.859375 cm²

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

Where can I download the Knowunity app?

You can download the app from Google Play Store and 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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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

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Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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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

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Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

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

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user