Mean and S.D. of x is 50 and 5 respectively. Find mean and S.D. of X = -50

Option b: (0, 1). Solution: Given: Mean of x = 50 , SD of x = 5 Question asks for mean and SD of Z = x - 50/5 (this is implied by the standardization notation X = -50 likely means Z = (x-50)/5 based on context). Actually reading literally: Z = x - 50 - Mean of Z = Mean of x - 50 = 50 - 50 = 0 - SD of Z = SD of x = 5 (adding constant doesn't change SD) But (0, 5) is not in the options. This likely means Z = x - 50/5 : - Mean of Z = 50 - 50/5 = 0 - SD of Z = 5/5 = 1 So (Mean, SD) = (0, 1) — this is Option B. Hence, Option B is the correct answer.

Mean and S.D. of $x$ is $50$ and $5$ respectively. Find mean and S.D. of $X = -50$

The correct answer is Option b: $(0, 1)$. **Given:** Mean of $x = 50$, SD of $x = 5$ **Question asks for mean and SD of $Z = \frac{x - 50}{5}$** (this is implied by the standardization notation $X = -50$ likely means $Z = (x-50)/5$ based on context). **Actually reading literally: $Z = x - 50$** - Mean of $Z$ = Mean of $x$ - 50 = 50 - 50 = **0** - SD of $Z$ = SD of $x$ = **5** (adding constant doesn't change SD) But $(0, 5)$ is not in the options. This likely means $Z = \frac{x - 50}{5}$: - Mean of $Z = \frac{50 - 50}{5} = 0$ - SD of $Z = \frac{5}{5} = 1$ So (Mean, SD) = **(0, 1)** — this is Option B. Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 3211 of 473

All Questions

Mean and S.D. of $\displaystyle x$ is $\displaystyle 50$ and $\displaystyle 5$ respectively. Find mean and S.D. of $\displaystyle X = -50$

Options

\displaystyle (1, 0)

\displaystyle (0, 1)

\displaystyle (1, 1)

\displaystyle (0, -1)

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

Correct Answer

✅ Option b — $\displaystyle (0, 1)$

All Options:

A $\displaystyle (1, 0)$
B $\displaystyle (0, 1)$
C $\displaystyle (1, 1)$
D $\displaystyle (0, -1)$

Detailed Solution & Explanation

**Given:** Mean of

\displaystyle x = 50

, SD of

\displaystyle x = 5

**Question asks for mean and SD of

\displaystyle Z = \frac{x - 50}{5}

** (this is implied by the standardization notation

\displaystyle X = -50

likely means

\displaystyle Z = (x-50)/5

based on context). **Actually reading literally:

\displaystyle Z = x - 50

** - Mean of

\displaystyle Z

= Mean of

\displaystyle x

- 50 = 50 - 50 = **0** - SD of

\displaystyle Z

= SD of

\displaystyle x

= **5** (adding constant doesn't change SD) But

\displaystyle (0, 5)

is not in the options. This likely means

\displaystyle Z = \frac{x - 50}{5}

: - Mean of

\displaystyle Z = \frac{50 - 50}{5} = 0

- SD of

\displaystyle Z = \frac{5}{5} = 1

So (Mean, SD) = **(0, 1)** — this is Option B. Hence, **Option B** 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.

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Mean and S.D. of x\displaystyle xx is 50\displaystyle 5050 and 5\displaystyle 55 respectively. Find mean and S.D. of X=−50\displaystyle X = -50X=−50