Find the mean of the following data using assumed mean method:

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Solution

Here, $A = 42$
$C l a s s e s$ $C l a s s - m a r k$
$x_{i}$ $f_{i}$ $d_{i} = x_{i} - A$ $f_{i} d_{i}$
$24.5 - 29.5$ $27$ $14$ $- 15$ $- 210$
$29.5 - 34.5$ $32$ $22$ $- 10$ $- 220$
$34.5 - 39.5$ $37$ $16$ $- 5$ $- 80$
$39.5 - 44.5$ $42$ $6$ $0$ $0$
$44.5 - 49.5$ $47$ $5$ $5$ $25$
$49.5 - 54.5$ $52$ $3$ $10$ $30$
$54.5 - 59.5$ $57$ $4$ $15$ $60$
$\sum f_{i} = 70$ $\sum f_{i} d_{i} = - 395$
$\Rightarrow$ $M e a n = A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$

$= 42 + \frac{(- 395)}{70}$
$= 42 - 5.64$
$= 36.36$

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$C l a s s e s$	$C l a s s - m a r k$ $x_{i}$	$f_{i}$	$d_{i} = x_{i} - A$	$f_{i} d_{i}$
$24.5 - 29.5$	$27$	$14$	$- 15$	$- 210$
$29.5 - 34.5$	$32$	$22$	$- 10$	$- 220$
$34.5 - 39.5$	$37$	$16$	$- 5$	$- 80$
$39.5 - 44.5$	$42$	$6$	$0$	$0$
$44.5 - 49.5$	$47$	$5$	$5$	$25$
$49.5 - 54.5$	$52$	$3$	$10$	$30$
$54.5 - 59.5$	$57$	$4$	$15$	$60$
		$\sum f_{i} = 70$		$\sum f_{i} d_{i} = - 395$