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SDCalc
KatamtamanMga Aplikasyon·11 min

Pagbuo ng Confidence Intervals Gamit ang Standard Deviation

Alamin kung paano bumuo ng mga confidence interval gamit ang standard deviation. Unawain kung ano ang ibig sabihin ng confidence levels at kung paano i-interpret ang CI sa mga senaryo sa totoong mundo.

Ano ang Confidence Interval?

Ang confidence interval (CI) ay isang saklaw ng mga halaga na malamang na naglalaman ng tunay na population parameter. Sa halip na magbigay ng iisang point estimate, kinikilala ng CI ang kawalan ng katiyakan sa pamamagitan ng pagbibigay ng isang saklaw.

“95% tayo na kumpiyansa na ang tunay na mean ay nasa pagitan ng 48.2 at 51.8”

95% CI: [48.2, 51.8]

Ang Formula

Ang confidence interval para sa isang population mean ay:

Formula ng Confidence Interval

CI = x̄ ± z* × (σ / √n)
  • x̄ = sample mean
  • z* = critical value (1.96 para sa 95% CI)
  • σ = standard deviation
  • n = laki ng sample
  • σ/√n = standard error
Antas ng KumpiyansaHalaga ng z*
90%1.645
95%1.960
99%2.576

Tamang Interpretasyon

Karaniwang Maling Akala

Ang 95% CI ay HINDI nangangahulugang “may 95% na probability na ang tunay na mean ay nasa interval na ito.” Ang tunay na mean ay nasa o wala sa interval—fixed ito.

Tamang Interpretasyon

“Kung paulit-ulit nating gagawin ang proseso ng sampling na ito, 95% ng mga kalkuladong interval ang maglalaman ng tunay na population mean.”

Mga Worked na Halimbawa

Halimbawa: Kasiyahan ng Customer

Nag-survey ka ng 100 customers at nakakita ng mean satisfaction score na 7.5 na may standard deviation na 1.5. Kalkulahin ang 95% CI.
1

Hanapin ang standard error

SE = 1.5 / √100 = 0.15
2

Kalkulahin ang margin of error

ME = 1.96 × 0.15 = 0.294
3

Buuin ang interval

CI = 7.5 ± 0.294 = [7.21, 7.79]

Interpretasyon: 95% tayo na kumpiyansa na ang tunay na mean na kasiyahan ng customer ay nasa pagitan ng 7.21 at 7.79.

Ano ang Nakaaapekto sa Lapad ng CI?

Laki ng Sample (n)

Mas malaking n = mas makitid na CI Mas maraming datos = mas tumpak

Standard Deviation (σ)

Mas malaking σ = mas malawak na CI Mas maraming variability = mas mababang katiyakan

Antas ng Kumpiyansa

Mas mataas na kumpiyansa = mas malawak na CI 99% CI ay mas malawak kaysa 95% CI

Further Reading

← Learning Center

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 goalWhat to focus onCommon mistake
DefinitionWhat the metric is and what quantity it summarizesTreating the formula as self-explanatory
Formula choiceSample versus population assumptions and notationUsing n when n-1 is required or vice versa
InterpretationWhether the result indicates concentration, spread, or riskCalling 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.