If the variables x and z are so related that z = ax+b for each where a and b are constant, then z = ax+b .

Option a: True. Solution: Step 1: Recall the property of arithmetic mean under linear transformation. If z = ax + b for every observation, then by the linearity of the arithmetic mean: z = ax + b Step 2: Apply to the given relation. Since z = ax + b holds for each value, the mean z satisfies: z = ax + b This is exactly the statement z = ax + b , which is True. Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ May 18Question 2853 of 473

All Questions

If the variables $\displaystyle x$ and $\displaystyle z$ are so related that $\displaystyle z = ax+b$ for each where $\displaystyle a$ and $\displaystyle b$ are constant, then $\displaystyle z = ax+b$ .

Options

ATrue

BFalse

CBoth

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — True

All Options:

ATrue
BFalse
CBoth
DNone of these

Detailed Solution & Explanation

**Step 1: Recall the property of arithmetic mean under linear transformation.** If

\displaystyle z = ax + b

for every observation, then by the linearity of the arithmetic mean:

\bar{z} = a\bar{x} + b

**Step 2: Apply to the given relation.** Since

\displaystyle z = ax + b

holds for each value, the mean

\displaystyle \bar{z}

satisfies:

\bar{z} = a\bar{x} + b

This is exactly the statement

\displaystyle \bar{z} = a\bar{x} + b

, which is **True**. Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central Tendency Fiscal Policy vs Monetary Policy: CA Foundation Economics

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If the variables x\displaystyle xx and z\displaystyle zz are so related that z=ax+b\displaystyle z = ax+bz=ax+b for each where a\displaystyle aa and b\displaystyle bb are constant, then z=ax+b\displaystyle z = ax+bz=ax+b.