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GCSE & A-Level Notes
06/12/2025
Psychology
Standard Deviation - Research Methods -
179
•
6 Dec 2025
•
A comprehensive guide to calculating standard deviation in psychology,... Show more
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_1.webp&w=2048&q=75)
Standard deviation serves as a crucial statistical tool in psychological research and data analysis.
Highlight: Standard deviation measures the average deviation of scores from the mean, providing insight into data distribution patterns.
Definition: The standard deviation indicates how far values in a dataset typically deviate from the mean, offering a standardized measure of spread.
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_2.webp&w=2048&q=75)
The mathematical foundation for calculating standard deviation is presented through its formal equation.
Definition: S = √
Vocabulary:
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_3.webp&w=2048&q=75)
A systematic approach to calculating standard deviation is outlined through six essential steps.
Highlight: The process involves:
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_4.webp&w=2048&q=75)
This section demonstrates the first step in calculating standard deviation using a practical example.
Example: Using the numbers 75, 83, 96, 100, 121, and 125:
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_5.webp&w=2048&q=75)
The process of finding deviations from the mean is explained with practical calculations.
Example: Deviations from mean (100):
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_6.webp&w=2048&q=75)
This section shows how to square the deviations to eliminate negative values.
Example: Squared deviations:
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_7.webp&w=2048&q=75)
The process of adding all squared deviations is demonstrated.
Example: Total sum of squares: 625 + 289 + 16 + 0 + 441 + 625 = 1996
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_8.webp&w=2048&q=75)
The calculation of variance is shown through division of the sum of squares.
Example: Variance calculation: 1996 ÷ 6 = 332.67
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_9.webp&w=2048&q=75)
The final step of calculating the square root of variance is demonstrated.
Example: Standard deviation = √332.67 = 18.2
![0
a° = 1[a0]
α
tan
()()。
Arcsic
Standard Deviation
+ Meaning:
• Measures the average amount that all scores deviate from the mean.
• The st](/_next/image?url=https%3A%2F%2Fcontent-eu-central-1.knowunity.com%2FCONTENT%2FqTjvTMoOfkQlJTjiArSO_image_page_10.webp&w=2048&q=75)
The empirical rule for normal distribution is explained with percentages and standard deviations.
Definition: The empirical rule states that:
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Stefan S
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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
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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
iOS user
Best app on earth! no words because it’s too good
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 THE SCHOOLGPT. 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
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
Best app on earth! no words because it’s too good
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 THE SCHOOLGPT. 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
A comprehensive guide to calculating standard deviation in psychology, explaining its importance in data analysis and distribution understanding.
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Standard deviation serves as a crucial statistical tool in psychological research and data analysis.
Highlight: Standard deviation measures the average deviation of scores from the mean, providing insight into data distribution patterns.
Definition: The standard deviation indicates how far values in a dataset typically deviate from the mean, offering a standardized measure of spread.
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The mathematical foundation for calculating standard deviation is presented through its formal equation.
Definition: S = √
Vocabulary:
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A systematic approach to calculating standard deviation is outlined through six essential steps.
Highlight: The process involves:
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This section demonstrates the first step in calculating standard deviation using a practical example.
Example: Using the numbers 75, 83, 96, 100, 121, and 125:
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The process of finding deviations from the mean is explained with practical calculations.
Example: Deviations from mean (100):
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This section shows how to square the deviations to eliminate negative values.
Example: Squared deviations:
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The process of adding all squared deviations is demonstrated.
Example: Total sum of squares: 625 + 289 + 16 + 0 + 441 + 625 = 1996
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The calculation of variance is shown through division of the sum of squares.
Example: Variance calculation: 1996 ÷ 6 = 332.67
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The final step of calculating the square root of variance is demonstrated.
Example: Standard deviation = √332.67 = 18.2
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The empirical rule for normal distribution is explained with percentages and standard deviations.
Definition: The empirical rule states that:
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.
You can download the app from Google Play Store and Apple App Store.
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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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
Best app on earth! no words because it’s too good
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 THE SCHOOLGPT. 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
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
Best app on earth! no words because it’s too good
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 THE SCHOOLGPT. 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
Psychology
Sociology