The mean of the numbers a, b, 8, 5, 10 is 6 a | vedclass

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

Question

(A) Given the mean $\bar{x} = 6$ for the numbers $a, b, 8, 5, 10$,we have $\frac{a+b+8+5+10}{5} = 6$,which implies $a+b+23 = 30$,so $a+b = 7$.The vari

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(A) Given the mean $\bar{x} = 6$ for the numbers $a, b, 8, 5, 10$,we have $\frac{a+b+8+5+10}{5} = 6$,which implies $a+b+23 = 30$,so $a+b = 7$.The variance is given by $\sigma^{2} = \frac{\sum (x_i - \bar{x})^2}{n} = 6.8$.Substituting the values: $\frac{(a-6)^2 + (b-6)^2 + (8-6)^2 + (5-6)^2 + (10-6)^2}{5} = 6.8$.$(a-6)^2 + (b-6)^2 + 4 + 1 + 16 = 34$.$(a-6)^2 + (b-6)^2 = 13$.Since $b = 7-a$,we have $(a-6)^2 + (7-a-6)^2 = 13$,which simplifies to $(a-6)^2 + (1-a)^2 = 13$.$a^2 - 12a + 36 + 1 - 2a + a^2 = 13$ $\Rightarrow 2a^2 - 14a + 24 = 0$ $\Rightarrow a^2 - 7a + 12 = 0$.$(a-4)(a-3) = 0$,so $a=4$ or $a=3$. If $a=4, b=3$; if $a=3, b=4$.The mean deviation $M$ about the mean is $M = \frac{\sum |x_i - \bar{x}|}{n}$.$M = \frac{|a-6| + |b-6| + |8-6| + |5-6| + |10-6|}{5} = \frac{|a-6| + |b-6| + 2 + 1 + 4}{5}$.For $a=3, b=4$: $M = \frac{|3-6| + |4-6| + 7}{5} = \frac{3 + 2 + 7}{5} = \frac{12}{5}$.Thus,$25M = 25 	imes \frac{12}{5} = 60$.

The mean of the numbers $a, b, 8, 5, 10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean,then $25M$ is equal to

Similar Questions

If the coefficients of variation of two distributions are $40$ and $20$ and their variances are $144$ and $64$ respectively,then the mean of their arithmetic means is

For a frequency distribution,the $7^{th}$ decile is computed by the formula:

In a frequency distribution,if $d_i$ is the deviation of observations from $a$,and the mean is given by $\text{Mean} = a + \frac{\Sigma f_i d_i}{\Sigma f_i}$,then what is $a$?

While calculating the mean and variance of $10$ readings,a student wrongly used the reading $52$ for the correct reading $25$. He obtained the mean and variance as $45$ and $16$ respectively. Find the correct mean and the variance.

The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

Vedclass Test Series

Exam Paper Generator

Online Exam Module