In a data,if the number i is repeated i times | vedclass

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

Question

(C) Given that the number $i$ is repeated $i$ times for $i = 1, 2, \ldots, n$. The sum of the observations is $\sum_{i=1}^{n} i 	imes i = \sum_{i=1}^

Vedclass · Accepted Answer

$\frac{2n+1}{3}$

Vedclass · Answer

(C) Given that the number $i$ is repeated $i$ times for $i = 1, 2, \ldots, n$. The sum of the observations is $\sum_{i=1}^{n} i 	imes i = \sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$. The total number of observations is $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$. The mean $\bar{X}$ is given by the ratio of the sum of observations to the total number of observations: $\bar{X} = \frac{\sum i^2}{\sum i} = \frac{\frac{n(n+1)(2n+1)}{6}}{\frac{n(n+1)}{2}} = \frac{2n+1}{3}$.

In a data,if the number $i$ is repeated $i$ times for $i=1, 2, \ldots, n$,then the mean of the data is

Similar Questions

The median of $10, 14, 11, 9, 8, 12, 6$ is

Find the median of the sequence $^{2n}C_0, ^{2n}C_1, ^{2n}C_2, \dots, ^{2n}C_n$ (where $n$ is even).

$A$ school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections. The overall average of marks per student is:

Which of the following,in the case of discrete data,is not equal to the median?

The mean of discrete observations $y_1, y_2, \ldots, y_n$ is given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module