मध्यवर्तीट्यूटोरियल·15 min

Excel और Python में मानक विचलन की गणना

Excel (STDEV.S, STDEV.P) और Python (numpy, pandas, statistics) में मानक विचलन की गणना के लिए चरण-दर-चरण ट्यूटोरियल। कोड उदाहरणों के साथ।

Excel: अवलोकन

Microsoft Excel प्रतिदर्श और समष्टि दोनों मानक विचलनों की गणना के लिए अंतर्निहित फ़ंक्शन प्रदान करता है। ये फ़ंक्शन Excel के सभी आधुनिक संस्करणों में उपलब्ध हैं।

Excel फ़ंक्शन

फ़ंक्शन	प्रकार	विवरण
`STDEV.S()`	प्रतिदर्श	प्रतिदर्श मानक विचलन (n-1 से भाग देता है)
`STDEV.P()`	समष्टि	समष्टि मानक विचलन (N से भाग देता है)
`STDEV()`	प्रतिदर्श	पुराना फ़ंक्शन, STDEV.S जैसा ही
`STDEVP()`	समष्टि	पुराना फ़ंक्शन, STDEV.P जैसा ही

Excel उदाहरण

Excel Formulas

// Data in cells A1:A10
=STDEV.S(A1:A10)     // Sample SD
=STDEV.P(A1:A10)     // Population SD

// For specific values
=STDEV.S(4, 8, 6, 5, 3)    // Returns 1.924

// Ignoring text and logical values
=STDEV.S(A1:A10)    // Ignores text
=STDEVA(A1:A10)     // Includes text as 0

विशेषज्ञ सुझाव

अधिकांश वास्तविक विश्लेषणों के लिए STDEV.S का उपयोग करें। STDEV.P का उपयोग तभी करें जब आपको निश्चित हो कि आपके पास संपूर्ण समष्टि है।

Python: अवलोकन

Python मानक विचलन की गणना के कई तरीके प्रदान करता है। सबसे आम लाइब्रेरी हैं NumPy, Pandas और अंतर्निहित statistics मॉड्यूल।

NumPy का उपयोग

Python (NumPy)

import numpy as np

data = [4, 8, 6, 5, 3]

# Population standard deviation (default)
pop_sd = np.std(data)
print(f"Population SD: {pop_sd}")  # 1.720

# Sample standard deviation
sample_sd = np.std(data, ddof=1)
print(f"Sample SD: {sample_sd}")  # 1.924

ddof क्या है?

ddof का अर्थ है “Delta Degrees of Freedom” (डेल्टा स्वतंत्रता कोटि)। ddof=1 सेट करने से NumPy को प्रतिदर्श SD के लिए (n-1) से भाग देने का निर्देश मिलता है। डिफ़ॉल्ट ddof=0 समष्टि SD देता है।

Pandas का उपयोग

Python (Pandas)

import pandas as pd

# Create a DataFrame
df = pd.DataFrame({'scores': [85, 90, 78, 92, 88]})

# Sample SD (default in pandas)
sample_sd = df['scores'].std()
print(f"Sample SD: {sample_sd}")

# Population SD
pop_sd = df['scores'].std(ddof=0)
print(f"Population SD: {pop_sd}")

# Multiple columns at once
df.std()  # Returns SD for all numeric columns

त्वरित तुलना

उपकरण	प्रतिदर्श SD	समष्टि SD
Excel	`STDEV.S()`	`STDEV.P()`
NumPy	`np.std(data, ddof=1)`	`np.std(data)`
Pandas	`df.std()`	`df.std(ddof=0)`
Python statistics	`stdev()`	`pstdev()`

How to Read This Article

A statistics tutorial is a practical interpretation guide, not just a formula dump. It refers to the assumptions, notation, and reporting language that analysts need when they explain a result to a teacher, manager, client, or reviewer. The article body covers the specific topic, while the sections below create a common interpretation frame that readers can reuse across related metrics.

Reading goal	What to focus on	Common mistake
Definition	What the metric is and what quantity it summarizes	Treating the formula as self-explanatory
Formula choice	Sample versus population assumptions and notation	Using n when n-1 is required or vice versa
Interpretation	Whether the result indicates concentration, spread, or risk	Calling a large value good or bad without context

Frequently Asked Questions

How should I interpret a high standard deviation?

A high standard deviation means the observations are spread farther from the mean on average. Whether that spread is acceptable depends on the context: wide dispersion might signal risk in finance, instability in manufacturing, or genuine natural variation in scientific data.

Why do some articles mention n while others mention n-1?

The denominator reflects the difference between population and sample formulas. Population variance and population standard deviation use N because the full dataset is known. Sample variance and sample standard deviation often use n-1 because Bessel’s correction reduces bias when estimating population spread from a sample.

What is a statistical interpretation guide?

A statistical interpretation guide is a page that moves beyond arithmetic and explains meaning. It tells you what a metric is, when the formula applies, and how to describe the result in plain English without overstating certainty.

Can I cite this article in a report?

You should cite the underlying authoritative reference for formal work whenever possible. This page is best used as an explanatory bridge that helps you understand the concept before quoting the original standard or handbook.

Why include direct citations on every article page?

Direct citations give readers a route to verify the definition, notation, and assumptions. That improves trust and reduces the chance that a simplified explanation is mistaken for the entire technical standard.

Authoritative References

These sources define the concepts referenced most often across our articles. Bessel's correction is a sample adjustment, variance is a squared measure of spread, and standard deviation is the square root of variance expressed in the same units as the data.