Basic Question in Statistics

[Amarjeet Jayanthi]

Dear All,

My name is Amarjeet Jayanthi.I am very weak in Statistics and Statistical concepts.Moreover,I cannot read and comprehend.

Please suggest me a way of how I can learn and cement the basic underlying concepts of Statistics.

I have a quick question.

Why is the formula for z-value z=(x-mu)/sigma?

Thanks a lot for your help.

I plan to learn data science.

Thanks,

Amarjeet

[indrajit khandai]

The formula z = (x - μ) / σ is used to calculate a z-score, which standardizes any value (x) from a normal distribution with mean (μ) and standard deviation (σ) into a value on the standard normal distribution (a distribution with a mean of 0 and a standard deviation of 1). This process allows for easy comparison of data points from different distributions by indicating how many standard deviations x is from the mean. 

Purpose of the Formula

• Standardization:The formula transforms any normal distribution into a standard normal distribution, which has a mean of 0 and a standard deviation of 1. 
• Comparison of Data:Z-scores allow you to compare different data points from different datasets, even if they have different means and standard deviations. 
• Understanding Position:A positive z-score means the value x is above the mean, while a negative z-score indicates it's below the mean. 

How the Formula Works

1. Subtract the Mean (x - μ): This step calculates the difference between the individual data point (x) and the mean (μ) of its distribution. This difference tells you how far x is from the mean, in the original units of the data.
2. Divide by the Standard Deviation (/ σ): This step divides the difference by the standard deviation (σ). This scales the result, effectively converting the raw difference into a number of standard deviations, which is the z-score. 

In Summary
The z-score formula essentially answers the question: "How many standard deviations is this specific data point (x) away from the mean (μ)?". 

--
The members of this group are expected to follow the following Protocols:
1. Please search previous posts in the group before posting the question.
2. Don't write the query in someone's post. Always use the option of New topic for the new question. You can do this by writing to dataanaly...@googlegroups.com
3. It’s better to give a proper subject to your post/query. It'll help others while searching.
4. Never write Open-ended queries. This group intends to help research scholars, NOT TO WORK FOR THEM.
5. Never write words like URGENT in your posts. People will help when they are free.
6. Never upload any information about National Seminars/Conferences. Send such information
in personal emails and feel free to share any RESEARCH-related information.
7. No Happy New Year, Happy Diwali, Happy Holi, Happy Birthday, Happy Anniversary, etc. allowed in this group.
8. Asking or sharing Research Papers is NOT ALLOWED.
9. You can share your questionnaire only once.
---
You received this message because you are subscribed to the Google Groups "DataAnalysis" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dataanalysistrai...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/dataanalysistraining/177804c2-df23-479e-ad47-60851af24709n%40googlegroups.com.

[Arvind Vidyarthy]

Hi Amarjeet,

Search for a "Basic Statistics" course on YouTube; many are freely available. Alternatively, you can follow the NPTEL website for the Basic Business Statistics course (designed for the Management discipline). Be patient and diligently complete at least one full Basic Statistics course, either from NPTEL or a YouTube course of your choice. Here r some suggestions u can try this (NPTEL, Youtube).

Coming back to u r question:

The formula you provided is used to calculate the Z-score. When analyzing raw data, we often find that the data distribution does not follow a consistent pattern. To facilitate meaningful analysis, we need a standardized point of comparison. The Z-score formula achieves this by comparing a data point to a Gaussian distribution (also known as the normal distribution). Specifically, the term (x - mu) represents the distance between the data point and the population mean (mu). And by dividing this difference by the standard deviation (sigma) scales the distance into units of standard deviation. This standardization allows us to compare data points across distributions, as the Z-score indicates how many standard deviations a data point is above (if positive) or below (if negative) the mean. 

Z-scores are most effective for approximately normal distributions but can also be applied more broadly for standardization purposes.

--

The members of this group are expected to follow the following Protocols:
1. Please search previous posts in the group before posting the question.
2. Don't write the query in someone's post. Always use the option of New topic for the new question. You can do this by writing to dataanaly...@googlegroups.com
3. It’s better to give a proper subject to your post/query. It'll help others while searching.
4. Never write Open-ended queries. This group intends to help research scholars, NOT TO WORK FOR THEM.
5. Never write words like URGENT in your posts. People will help when they are free.
6. Never upload any information about National Seminars/Conferences. Send such information
in personal emails and feel free to share any RESEARCH-related information.
7. No Happy New Year, Happy Diwali, Happy Holi, Happy Birthday, Happy Anniversary, etc. allowed in this group.
8. Asking or sharing Research Papers is NOT ALLOWED.
9. You can share your questionnaire only once.
---
You received this message because you are subscribed to the Google Groups "DataAnalysis" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dataanalysistrai...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/dataanalysistraining/177804c2-df23-479e-ad47-60851af24709n%40googlegroups.com.

--

Thanks & Regards

Arvind Kumar Vidyarthy
Contact No: +91-9608791779
Ph.D. (Industrial Engg. & Management)
Indian Institute Of Technology (ISM), Dhanbad

[Neeraj Kaushik]

Dear Amarjeet

How about learning Statistics using dance movement?

Of course, only Prof Andy could think of this

https://www.youtube.com/playlist?list=PLEzw67WWDg82xKriFiOoixGpNLXK2GNs9

Happy Learning

Neeraj

--