Chapter 6: Q.6.114 (page 279)

Express the quartiles, $Q_{1}, Q_{2}$ , and $Q_{3}$ , of a normally distributed variable in terms of its mean, $μ$ , and standard deviation, $σ$ .

Short Answer

Expert verified

The required quartile,

Q_{1} = μ - 0.67 σ

$Q_{2} = μ$

$Q_{3} = μ + 0.67 σ$

Step by step solution

Given Information

Consider normally distributed variable.

Explanation

In a standard normal distribution,

The quartile $Q_{1}$ is the area under the curve that falls below $25 %$ of data.

The area to the left of the $z$ score $0.25$

$= 0.67$

\frac{x - μ}{σ} = - 0.67

Hence, $Q_{1} = μ - 0.67 σ$

Explanation

The quartile $Q_{2}$ is the area under the curve that falls below $25 %$ of data.

The area to the left of the $z$ score $0.50$ .

$= 0.0$

$\frac{x - μ}{σ} = 0$

$x = μ$

Hence, $Q_{2} = μ$

The quartile $Q_{3}$ is the area under the curve that falls below $75 %$ of data.

The area to the left of the $z$ score $0.75$

$= 0.67$

$\frac{x - μ}{σ} = 0.67$

$x = μ + 0.67 σ$

Hence, $Q_{3} = μ + 0.67 σ$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Express the quartiles, $Q_{1}, Q_{2}$ , and $Q_{3}$ , of a normally distributed variable in terms of its mean, $μ$ , and standard deviation, $σ$ .

Short Answer

Step by step solution

Given Information

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Logic and Functions

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Express the quartiles,Q1,Q2, and Q3, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.

Short Answer

Step by step solution

Given Information

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Logic and Functions

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Express the quartiles, $Q_{1}, Q_{2}$ , and $Q_{3}$ , of a normally distributed variable in terms of its mean, $μ$ , and standard deviation, $σ$ .