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Find the Mean, Variance, \u0026 Standard Deviation of Frequency Grouped Data Table| Step-by-Step Tutorial
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Learn how to find the mean, variance, and standard deviation of a frequency Grouped Data table. Simple and indepth explanation by PreMath.com
Standard Deviation – Explained and Visualized
The video above is more focused on the concept. This other one explains how it’s calculated: https://www.youtube.com/watch?v=WVx3MYdQ9w
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Video transcript:
\”Have we discovered a new particle in physics?
Is a manufacturing process out of control?
What percentage of men are taller than Lebron James? How about taller than Yao Ming?
All of these questions can be answered using the concept of standard deviation.
For any set of data, the mean and standard deviation can be calculated. For example, five people may have the following amounts of money in their wallets: 21, 50, 62, 85, and 90. The mean is $61.60 and the standard deviation is $28.01.
How much does the data vary from the average? Standard deviation is a measure of spread, that is, how spread out a set of data is.
A low standard deviation tells us that the data is closely clustered around the mean (or average), while a high standard deviation indicates that the data is dispersed over a wider range of values.
It is used when the distribution of data is approximately normal, resembling a bell curve.
Standard deviation is commonly used to understand whether a specific data point is “standard” and expected or unusual and unexpected. Standard deviation is represented by the lowercase greek letter sigma. A data point’s distance from the mean can be measured by the number of standard deviations that it is above or below the mean. A data point that is beyond a certain number of standard deviations from the mean represents an outcome that is significantly above or below the average. This can be used to determine whether a result is statistically significant or part of expected variation, such as whether a bottle with an extra ounce of soda is to be expected or warrants further investigation into the production line.
The 689599.7 rule tells us that about 68% of the data fall within one standard deviation of the mean. About 95% of data fall within two standard deviations of the mean. And about 99.7% of data fall within 3 standard deviations of the mean.
The average height of an American adult male is 5’10, with a standard deviation of 3 inches. Using the 689599.7 rule, this means that 68% of American men are 5’10 plus or minus 3 inches, 95% of American men are 5’10 plus or minus 6 inches, and 99.7% of American men are 5’10 plus or minus 9 inches. So, this means only about .3% of American men deviate more than 9 inches from the average, with .15% taller than 6’7 and .15% shorter than 5’1. This reasoning suggests that Lebron James is 1 in 2500 and Yao Ming is 1 in 450 million.
In particle physics, scientists have what are called 5sigma results, results that are five standard deviations above or below the mean. A result that varies this much can signify a discovery as it has only a 1 in 3.5 million chance that it is due to random fluctuation.
In summary, standard deviation is a measure of spread. Along with the mean, the standard deviation allows us to determine whether a value is statistically significant or part of expected variation.\”
Nghiên cứu định lượng và nghiên cứu định tính | TS.BS.Vũ Duy Kiên
👉Trong video này tôi sẽ hướng dẫn bạn phân biệt giữa Nghiên cứu định lượng và nghiên cứu định tính.
👉Khi tiến hành nghiên cứu bạn thường phải lựa chọn giữa nghiên cứu định lượng và định tính. Thực tế, để quyết định được loại nghiên cứu nào khi tiến hành nghiên cứu cần phải dựa vào chủ đề nghiên cứu, câu hỏi nghiên cứu, khả năng và kỹ năng của bạn đối với nghiên cứu. Trước hết chúng ta sẽ cũng nhau tìm hiểu xem định nghĩa của hai loại nghiên cứu này thế nào:
👉Nghiên cứu định lượng, trong tiếng Anh là Quantitative Research, là nghiên cứu giải thích hiện tượng dựa trên việc phân tích các số liệu. Số liệu thu thập được là số liệu số được phân tích bằng các phương pháp toán học và thống kê. Có một định nghĩa tiếng Anh mà tôi thấy tương đối rõ ràng và dễ hiểu, bạn có thể tham khảo ở đây: “Quantitative research is “explaining phenomena by collecting numerical data that are analysed using mathematically based methods (in particular statistics).”.
👉Nghiên cứu định tính, trong tiếng Anh là Qualitative Research, là nghiên cứu để trả lời câu hỏi tại sao và làm thế nào con người lại hành xử theo cái cách mà họ đã làm. Cụ thể hơn, nghiên cứu định tính cung cấp các thông tin chuyên sâu về cách ứng xử của con người. Bạn cũng có thể dùng định nghĩa tiếng Anh như sau: “Qualitative research seeks to answer questions about why and how people behave in the way that they do. It provides indepth information about human behaviour.”.
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