If y = 3 + (4.5)x and the mode for x - value is 20 , then the mode for y - value is

Option d: 93. Solution: Step 1: Recall the property of mode under linear transformation. If y = a + bx , then Mode (y) = a + b × Mode (x) . Step 2: Given information. - y = 3 + 4.5x - Mode of x = 20 Step 3: Calculate mode of y . Mode(y) = 3 + 4.5 × 20 = 3 + 90 = 93 So Mode( y ) = 93 , which corresponds to Option D. However, the given correct answer is B ( 12 ). Let us re-examine: perhaps the question means y = 3 + 4.5x but the actual relationship should be read differently, or perhaps it's y = (3 + 4.5)x = 7.5x which gives 7.5 × 20 = 150 — that doesn't match either. Alternatively, maybe the relationship is y = 3/4.5 + x or something else. Given the options, let's check option D: 3 + 4.5 × 20 = 93 ✓ (Option D). Computing directly: Mode (y) = 3 + 4.5 × 20 = 93 . Hence, Option D is the correct answer.

If $y = 3 + (4.5)x$ and the mode for $x$ - value is $20$, then the mode for $y$ - value is

The correct answer is Option d: $93$. **Step 1: Recall the property of mode under linear transformation.** If $y = a + bx$, then Mode$(y)$ = $a + b \times$ Mode$(x)$. **Step 2: Given information.** - $y = 3 + 4.5x$ - Mode of $x = 20$ **Step 3: Calculate mode of $y$.** $$\text{Mode}(y) = 3 + 4.5 \times 20 = 3 + 90 = 93$$ So Mode($y$) = $93$, which corresponds to **Option D**. However, the given correct answer is B ($12$). Let us re-examine: perhaps the question means $y = 3 + 4.5x$ but the actual relationship should be read differently, or perhaps it's $y = (3 + 4.5)x = 7.5x$ which gives $7.5 \times 20 = 150$ — that doesn't match either. Alternatively, maybe the relationship is $y = \frac{3}{4.5} + x$ or something else. Given the options, let's check option D: $3 + 4.5 \times 20 = 93$ ✓ (Option D). Computing directly: Mode$(y) = 3 + 4.5 \times 20 = 93$. Hence, **Option D** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Jan. 21Question 2994 of 473

All Questions

If $\displaystyle y = 3 + (4.5)x$ and the mode for $\displaystyle x$ - value is $\displaystyle 20$ , then the mode for $\displaystyle y$ - value is

Options

\displaystyle 3.225

\displaystyle 12

\displaystyle 24.5

\displaystyle 93

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

Correct Answer

✅ Option d — $\displaystyle 93$

All Options:

A $\displaystyle 3.225$
B $\displaystyle 12$
C $\displaystyle 24.5$
D $\displaystyle 93$

Detailed Solution & Explanation

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

\displaystyle y = a + bx

, then Mode

\displaystyle (y)

\displaystyle a + b \times

Mode

\displaystyle (x)

. **Step 2: Given information.** -

\displaystyle y = 3 + 4.5x

- Mode of

\displaystyle x = 20

**Step 3: Calculate mode of

\displaystyle y

.**

\text{Mode}(y) = 3 + 4.5 \times 20 = 3 + 90 = 93

So Mode(

\displaystyle y

) =

\displaystyle 93

, which corresponds to **Option D**. However, the given correct answer is B (

\displaystyle 12

). Let us re-examine: perhaps the question means

\displaystyle y = 3 + 4.5x

but the actual relationship should be read differently, or perhaps it's

\displaystyle y = (3 + 4.5)x = 7.5x

which gives

\displaystyle 7.5 \times 20 = 150

— that doesn't match either. Alternatively, maybe the relationship is

\displaystyle y = \frac{3}{4.5} + x

or something else. Given the options, let's check option D:

\displaystyle 3 + 4.5 \times 20 = 93

✓ (Option D). Computing directly: Mode

\displaystyle (y) = 3 + 4.5 \times 20 = 93

. Hence, **Option D** 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.

Key Concepts to Understand

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

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If y=3+(4.5)x\displaystyle y = 3 + (4.5)xy=3+(4.5)x and the mode for x\displaystyle xx - value is 20\displaystyle 2020, then the mode for y\displaystyle yy - value is

Options

Correct Answer

All Options:

Detailed Solution & Explanation

About This Chapter: Measures of Central Tendency and Dispersion

Key Concepts to Understand

Mode

Related Comparison Tables

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If $\displaystyle y = 3 + (4.5)x$ and the mode for $\displaystyle x$ - value is $\displaystyle 20$ , then the mode for $\displaystyle y$ - value is