If the mean of 4, 7, 2, 8, 6 and a is 7,then | vedclass

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

Question

(D) Given observations are $4, 7, 2, 8, 6, a$ and the mean is $7$.We know that Mean $= \frac{4 + 7 + 2 + 8 + 6 + a}{6}$.$7 = \frac{27 + a}{6}$ $\Right

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Given observations are $4, 7, 2, 8, 6, a$ and the mean is $7$.We know that Mean $= \frac{4 + 7 + 2 + 8 + 6 + a}{6}$.$7 = \frac{27 + a}{6}$ $\Rightarrow 42 = 27 + a$ $\Rightarrow a = 15$.Now,the observations in ascending order are $2, 4, 6, 7, 8, 15$.Since the number of observations $n = 6$ (even),the median is the average of the $3^{rd}$ and $4^{th}$ observations.Median $= \frac{6 + 7}{2} = 6.5$.Mean deviation from median $= \frac{\sum |x_i - 6.5|}{6}$.$= \frac{|2 - 6.5| + |4 - 6.5| + |6 - 6.5| + |7 - 6.5| + |8 - 6.5| + |15 - 6.5|}{6}$.$= \frac{4.5 + 2.5 + 0.5 + 0.5 + 1.5 + 8.5}{6} = \frac{18}{6} = 3$.

Marks obtained	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Number of students	$10$	$8$	$12$	$9$	$11$

$x_i$	$5$	$10$	$15$	$20$	$25$
$f_i$	$7$	$4$	$6$	$3$	$5$

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$,then the mean deviation from the median of these observations is

Similar Questions

Let $\bar{X}$ and $M.D.$ be the mean and the mean deviation about $\bar{X}$ of $n$ observations $x_i,$ $i = 1, 2, \dots, n.$ If each of the observations is increased by $5,$ then the new mean and the mean deviation about the new mean,respectively,are

Find the mean deviation about the mean for the following data:
Marks obtained $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
Number of students $10$ $8$ $12$ $9$ $11$

Find the mean deviation about the mean for the given data:

$x_i$ $5$ $10$ $15$ $20$ $25$

$f_i$ $7$ $4$ $6$ $3$ $5$

What is the coefficient of mean deviation about the median for the observations $40, 62, 54, 90, 68, 76$?

If $a_0, a_1, \ldots, a_{11}$ are in an arithmetic progression with common difference $d$,then their mean deviation from their arithmetic mean is

Vedclass Test Series

Exam Paper Generator

Online Exam Module