CUET PG 2021 — Mathematics PYQ

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Question

CUET PG 2021 — Mathematics PYQ

CUET PG | Mathematics | 2021

If the standard deviation of x,y and z is p, then the standard deviation of 3x +5, 3y + 5, 3z + 5 is

Choose the correct answer:

Explanation

Step 1: Diya gaya hai ki $x, y, z$ ka standard deviation $p$ hai.

SD(x, y, z) = p

Step 2: Humein naye set $\{3x+5, 3y+5, 3z+5\}$ ka standard deviation nikalna hai. Yahan transformation hai:

X_{new} = 3X + 5

Step 3: Property lagate hain:

Yahan $+5$ (Addition) ka koi asar nahi hoga.
Yahan $3$ (Multiplication) se standard deviation guna ho jayega.

Isliye:

SD(3x+5, 3y+5, 3z+5) = 3 \times SD(x, y, z)

SD_{new} = 3 \times p

SD_{new} = 3p