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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 🇺🇸

1 document

1 / 3

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Don't miss anything!

Exploring Data: Distributions

•

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

(outliers).

•

Mean:

𝑥=∑𝑥

𝑛=𝑥1+𝑥2+⋯+𝑥𝑛

𝑛

•

Standard deviation:

𝑠=√∑(𝑥−𝑥)2

𝑛−1

•

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 = Q3 - Q1

•

Five-number summary:

o

Minimum, Q1, M, Q3, Maximum

•

If X has mean µ and standard deviation σ:

𝑧=𝑥−𝜇

𝜎 and 𝑥 = 𝜇 + 𝑧∗ 𝜎

Binomial Distribution:

•

𝐸(𝑋)=𝑛𝑝

•

𝑆𝐷(𝑋)=√𝑛𝑝𝑞

Sampling Distribution of a Sample Proportion

•

The sample proportion, 𝑝, is

𝑝=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑒𝑠

𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 =𝑥

𝑛

•

𝜇𝑝=𝐸(𝑝)=𝑝

•

𝜎𝑝=𝑆𝐷(𝑝)=√𝑝𝑞

𝑛

•

The distribution of 𝑝 can be approximated by a Normal if

▪ The sample is random, and

▪ 𝑛𝑝≥10 𝒂𝒏𝒅 𝑛𝑞≥10

•

The standardized value of 𝑝 is 𝑧=𝑝−𝑝

√𝑝𝑞

𝑛

Sampling Distribution of a Sample Mean

•

𝜇𝑋

=𝐸(𝑋

)=𝜇

•

𝜎𝑋

=𝑆𝐷(𝑋

)=𝜎

√𝑛

•

The distribution of 𝑋

 can be approximated by a Normal if

▪ The sample is random, and

▪ The CLT applies:

• Parent population is Normal, or

• 𝑛≥30

•

The standardized value of 𝑋

 is 𝑧=𝑥−𝜇

𝜎

√𝑛

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

𝑛

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 μ and standard deviation σ:

𝑥−𝜇

𝜎

and 𝑥 = 𝜇 + 𝑧 ∗ 𝜎

Binomial Distribution:

Sampling Distribution of a Sample Proportion

The sample proportion, 𝑝̂ , is

𝑝̂

𝑝𝑞

𝑛

The distribution of 𝑝̂ can be approximated by a Normal if

▪ The sample is random, and

The standardized value of 𝑝̂ is 𝑧 =

𝑝

̂ −𝑝

√

𝑝𝑞

𝑛

Sampling Distribution of a Sample Mean

𝑋

̅

𝑋

̅

𝜎

√𝑛

The distribution of 𝑋

can be approximated by a Normal if

▪ The sample is random, and

▪ The CLT applies:

Parent population is Normal, or

The standardized value of 𝑋

is 𝑧 =

𝑥̅ −𝜇

𝜎

√𝑛

Confidence Intervals for a Proportion

The conditions to perform a CI for 𝑝:

▪ The sample is random, and

CI formula:

𝛼

2

Hypothesis Test for a Proportion

The conditions to perform a HT for 𝑝:

▪ The sample is random, and

Test statistic formula:

∗

Confidence Intervals for a Mean

The conditions to perform a CI for 𝜇:

▪ The sample is random, and

▪ The CLT applies:

Parent population is Normal, or

CI formula: 𝑥̅ ± |𝑡

𝛼

2

,𝑑𝑓

𝑠

√

𝑛

Hypothesis Test for a Mean

The conditions to perform a HT for 𝜇:

▪ The sample is random, and

▪ The CLT applies:

Parent population is Normal, or

Test statistic formula:

∗

Hypothesis Test for a Mean Difference

The conditions to perform a HT for 𝜇

𝑑

▪ The samples are random,

▪ The samples are dependent, and

▪ The CLT applies:

Parent population is Normal, or

Test statistic formula:

∗

𝑑

Common Values from the Standard Normal

05

025

01

005

Formula Sheet for Statistics, Cheat Sheet of Statistics

Related documents

Partial preview of the text

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

- Q

, M , Q