JEE 2023 — Mathematics PYQ

Solution

1. Di gayi jankari (Given Data):

• Observations ki sankhya $(n)=10$

• Galat mean $({\bar{x}}_w)=20$

• Galat standard deviation $({\sigma }_w)=8⟹$ Galat variance $({\sigma }_w^2)=64$

• Galat observation $=50$, Sahi observation $=40$

2. Sahi Mean (${\bar{x}}_c$) nikalna:

Galat sum $\sum x_w=n\times {\bar{x}}_w=10\times 20=200$

Sahi sum $\sum x_c=200-50+40=190$

Sahi mean ${\bar{x}}_c=\frac{190}{10}=19$

3. Sahi Variance (${\sigma }_c^2$) nikalna:

Variance ka formula hota hai: ${\sigma }^2=\frac{\sum x^2}{n}-(\bar{x}{)}^2$

Pehle galat $\sum x_w^2$ nikalte hain:

Ab sahi $\sum x_c^2$ nikalte hain:

Ab sahi variance nikalte hain:

Final Answer:

Correct variance 13 hai. Sahi vikalp (4) hai.