CA Foundation Exam  >  CA Foundation Questions  >  If Arithmetic mean and coefficient of variati... Start Learning for Free
If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?
Most Upvoted Answer
If Arithmetic mean and coefficient of variation of X are 5 and 20 resp...
Solution:

Given, Arithmetic Mean of X = 5

Coefficient of Variation of X = 20%

Let us assume X follows a Normal Distribution.

Step 1: Finding the Standard Deviation of X

Coefficient of Variation (CV) = (Standard Deviation / Arithmetic Mean) × 100

⇒ Standard Deviation of X = CV × Arithmetic Mean / 100

⇒ Standard Deviation of X = 20/100 × 5

⇒ Standard Deviation of X = 1

Step 2: Finding the Mean and Standard Deviation of 15 - 2X

Mean of 15 - 2X = 15 - 2 × Mean of X

⇒ Mean of 15 - 2X = 15 - 2 × 5

⇒ Mean of 15 - 2X = 5

Standard Deviation of 15 - 2X = 2 × Standard Deviation of X

⇒ Standard Deviation of 15 - 2X = 2 × 1

⇒ Standard Deviation of 15 - 2X = 2

Step 3: Finding the Variance of 15 - 2X

Variance of 15 - 2X = (Standard Deviation of 15 - 2X)^2

⇒ Variance of 15 - 2X = 2^2

⇒ Variance of 15 - 2X = 4

Therefore, the Variance of 15 - 2X = 4.
Community Answer
If Arithmetic mean and coefficient of variation of X are 5 and 20 resp...
First find out the sd of X.

See,

Coefficient of variation = SD/Mean*100%

Assuming CoV is given in percentage,

=> SD = Mean*COV = 10*40% = 4

=> Var(X) = 16

Var(15-2X) = 4*Var(X) = 4*16 = 64

Note: If the CoV is not given in percentage please adjust accordingly
Explore Courses for CA Foundation exam
If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?
Question Description
If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?.
Solutions for If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? in English & in Hindi are available as part of our courses for CA Foundation. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? defined & explained in the simplest way possible. Besides giving the explanation of If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?, a detailed solution for If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? has been provided alongside types of If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? theory, EduRev gives you an ample number of questions to practice If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? tests, examples and also practice CA Foundation tests.
Explore Courses for CA Foundation exam

Top Courses for CA Foundation

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev