Q.6.114 Express the quartiles,聽Q1,Q2, a... [FREE SOLUTION]

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, $渭$ , and standard deviation, $蟽$ .

Short Answer

Expert verified

The required quartile,

Q_{1} = 渭 - 0.67 蟽

$Q_{2} = 渭$

$Q_{3} = 渭 + 0.67 蟽$

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 - 渭}{蟽} = - 0.67

Hence, $Q_{1} = 渭 - 0.67 蟽$

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 $0.50$ .

$= 0.0$

$\frac{x - 渭}{蟽} = 0$

$x = 渭$

Hence, $Q_{2} = 渭$

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 $0.75$

$= 0.67$

$\frac{x - 渭}{蟽} = 0.67$

$x = 渭 + 0.67 蟽$

Hence, $Q_{3} = 渭 + 0.67 蟽$

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91影视

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

Short Answer

Step by step solution

Given Information

Explanation

Explanation

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91影视

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

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

Applied Mathematics

Calculus

Pure Maths

Probability and Statistics

Geometry

Statistics

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, $渭$ , and standard deviation, $蟽$ .