If x_1, x_2, ldots, x_n are n observations su | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) We know that the variance of a set of observations is always non-negative,i.e.,$\sigma^2 = \frac{\sum x_i^2}{n} - \left(\frac{\sum x_i}{n}\right)^

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(D) We know that the variance of a set of observations is always non-negative,i.e.,$\sigma^2 = \frac{\sum x_i^2}{n} - \left(\frac{\sum x_i}{n}\right)^2 \geq 0$. Given $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$. Substituting these values into the inequality: $\frac{400}{n} - \left(\frac{80}{n}\right)^2 \geq 0$ $\frac{400}{n} - \frac{6400}{n^2} \geq 0$ Multiplying by $n^2$ (since $n > 0$): $400n - 6400 \geq 0$ $400n \geq 6400$ $n \geq \frac{6400}{400}$ $n \geq 16$. Thus,the least value of $n$ is $16$.

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

Similar Questions

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

In the context of the lanthanoids,which of the following statements is not correct?

The Bulk modulus for an incompressible liquid is

Which among the following compounds has the highest boiling point?

Three bodies,a ring,a solid cylinder,and a solid sphere,roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module