Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Formula Sheet for Statistics, Cheat Sheet of Statistics

North Carolina State University (NCSU)Statistics

Formula Sheet for ST 311 at NCSU

Typology: Cheat Sheet

2024/2025

Uploaded on 01/05/2025

thomas-sierra-1
thomas-sierra-1 ๐Ÿ‡บ๐Ÿ‡ธ

1 document

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Exploring Data: Distributions
โ€ข
Evaluate overall pattern (shape, center, spread) and deviations
(outliers).
โ€ข
Mean:
๐‘ฅ๎ชง=โˆ‘๐‘ฅ
๐‘›=๐‘ฅ1+๐‘ฅ2+โ‹ฏ+๐‘ฅ๐‘›
๐‘›
โ€ข
Standard deviation:
๐‘ =โˆšโˆ‘(๐‘ฅโˆ’๐‘ฅ๎ชง)2
๐‘›โˆ’1
โ€ข
Quartiles:
o
The first quartile Q1 is the point with 25% of the data below it.
o
The median M is the point with 50% of the data below it.
o
The third quartile Q3 is the point with 25% of the data above it.
โ€ข
Interquartile range: IQR = Q3 - Q1
โ€ข
Five-number summary:
o
Minimum, Q1, M, Q3, Maximum
โ€ข
If X has mean ยต and standard deviation ฯƒ:
๐‘ง=๐‘ฅโˆ’๐œ‡
๐œŽ and ๐‘ฅ = ๐œ‡ + ๐‘งโˆ— ๐œŽ
Binomial Distribution:
โ€ข
๐ธ(๐‘‹)=๐‘›๐‘
โ€ข
๐‘†๐ท(๐‘‹)=โˆš๐‘›๐‘๐‘ž
Sampling Distribution of a Sample Proportion
โ€ข
The sample proportion, ๐‘๎žธ, is
๐‘๎žธ=๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘ ๐‘ข๐‘๐‘๐‘’๐‘ ๐‘ ๐‘’๐‘ 
๐‘ ๐‘Ž๐‘š๐‘๐‘™๐‘’ ๐‘ ๐‘–๐‘ง๐‘’ =๐‘ฅ
๐‘›
โ€ข
๐œ‡๐‘๏œ=๐ธ(๐‘๎žธ)=๐‘
โ€ข
๐œŽ๐‘๏œ=๐‘†๐ท(๐‘๎žธ)=โˆš๐‘๐‘ž
๐‘›
โ€ข
The distribution of ๐‘๎žธ can be approximated by a Normal if
โ–ช The sample is random, and
โ–ช ๐‘›๐‘โ‰ฅ10 ๐’‚๐’๐’… ๐‘›๐‘žโ‰ฅ10
โ€ข
The standardized value of ๐‘๎žธ is ๐‘ง=๐‘๏œโˆ’๐‘
โˆš๐‘๐‘ž
๐‘›
Sampling Distribution of a Sample Mean
โ€ข
๐œ‡๐‘‹
๏Œค=๐ธ(๐‘‹
๏Œค)=๐œ‡
โ€ข
๐œŽ๐‘‹
๏Œค=๐‘†๐ท(๐‘‹
๏Œค)=๐œŽ
โˆš๐‘›
โ€ข
The distribution of ๐‘‹
๏Œค can be approximated by a Normal if
โ–ช The sample is random, and
โ–ช The CLT applies:
โ€ข Parent population is Normal, or
โ€ข ๐‘›โ‰ฅ30
โ€ข
The standardized value of ๐‘‹
๏Œค is ๐‘ง=๐‘ฅ๎ชงโˆ’๐œ‡
๐œŽ
โˆš๐‘›
pf3

Partial preview of the text

Download Formula Sheet for Statistics and more Cheat Sheet Statistics in PDF only on Docsity!

Exploring Data: Distributions

  • Evaluate overall pattern (shape, center, spread) and deviations

(outliers).

  • Mean:

1

2

๐‘›

  • Standard deviation:

2

  • Quartiles:

o The first quartile Q1 is the point with 25% of the data below it.

o The median M is the point with 50% of the data below it.

o The third quartile Q3 is the point with 25% of the data above it.

  • Interquartile range: IQR = Q 3

- Q

1

  • Five-number summary:

o Minimum, Q 1

, M , Q

3

, Maximum

  • If X has mean ฮผ and standard deviation ฯƒ:

๐‘ฅโˆ’๐œ‡

๐œŽ

and ๐‘ฅ = ๐œ‡ + ๐‘ง โˆ— ๐œŽ

Binomial Distribution:

Sampling Distribution of a Sample Proportion

  • The sample proportion, ๐‘ฬ‚ , is

๐‘ฬ‚

๐‘ฬ‚

๐‘๐‘ž

๐‘›

  • The distribution of ๐‘ฬ‚ can be approximated by a Normal if

โ–ช The sample is random, and

  • The standardized value of ๐‘ฬ‚ is ๐‘ง =

๐‘

ฬ‚ โˆ’๐‘

โˆš

๐‘๐‘ž

๐‘›

Sampling Distribution of a Sample Mean

๐‘‹

ฬ…

๐‘‹

ฬ…

๐œŽ

โˆš๐‘›

  • The distribution of ๐‘‹

can be approximated by a Normal if

โ–ช The sample is random, and

โ–ช The CLT applies:

  • Parent population is Normal, or
  • The standardized value of ๐‘‹

is ๐‘ง =

๐‘ฅฬ… โˆ’๐œ‡

๐œŽ

โˆš๐‘›

Confidence Intervals for a Proportion

  • The conditions to perform a CI for ๐‘:

โ–ช The sample is random, and

  • CI formula:

๐›ผ

2

Hypothesis Test for a Proportion

  • The conditions to perform a HT for ๐‘:

โ–ช The sample is random, and

  • Test statistic formula:

โˆ—

Confidence Intervals for a Mean

  • The conditions to perform a CI for ๐œ‡:

โ–ช The sample is random, and

โ–ช The CLT applies:

  • Parent population is Normal, or
  • CI formula: ๐‘ฅฬ… ยฑ |๐‘ก

๐›ผ

2

,๐‘‘๐‘“

๐‘ 

โˆš

๐‘›

Hypothesis Test for a Mean

  • The conditions to perform a HT for ๐œ‡:

โ–ช The sample is random, and

โ–ช The CLT applies:

  • Parent population is Normal, or
  • Test statistic formula:

โˆ—

Hypothesis Test for a Mean Difference

  • The conditions to perform a HT for ๐œ‡

๐‘‘

โ–ช The samples are random,

โ–ช The samples are dependent, and

โ–ช The CLT applies:

  • Parent population is Normal, or
  • Test statistic formula:

โˆ—

๐‘‘

๐‘‘

Common Values from the Standard Normal

  1. 05
  1. 025
  1. 01
  1. 005