The point estimate of the population standard deviation… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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The point estimate of the population standard deviation for the random sample 5, 8, 10, 7, 10, 14 is:

Official previous-year question

Held on 16 May 2025 · Verified 13 Jul 2026.

Options

A
1.5
B
4.9
C
3.1
D
9

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Solution

A function is decreasing when its derivative is negative, i.e., when $f'(x) < 0$ .

Given: $f(x) = \frac{3}{x} + 7$

Rewriting: $f(x) = 3x^{-1} + 7$

Using the power rule:

$f'(x) = 3 \cdot (-1) \cdot x^{-2} + 0$

$f'(x) = -3x^{-2}$

$f'(x) = -\frac{3}{x^2}$

For the function to be decreasing: $f'(x) < 0$

$-\frac{3}{x^2} < 0$

Since $x^2$ is always positive for any $x \neq 0$ , the expression $-\frac{3}{x^2}$ is always negative.

Therefore, $f'(x) < 0$ for all $x \in \mathbb{R} - \{0\}$ .

The function $f(x) = \frac{3}{x} + 7$ is decreasing for $x \in \mathbb{R} - \{0\}$ .

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