Find the mean of the following frequency distribution by the assumed mean method :
No. of apples $50 - 53$ $53 - 56$ $56 - 59$ $59 - 62$ $62 - 65$
No of boxes $20$ $150$ $115$ $95$ $20$

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Solution

$N o . o f a p p l e s$ $x_{i}$ $f_{i}$ $d_{i} = x_{i} - A$ $f_{i} d_{i}$
$50 - 53$ $51.5$ $20$ $- 6$ $- 120$
$53 - 56$ $54.5$ $150$ $- 3$ $- 450$
$56 - 59$ $57.5 = A$ $115$ $0$ $0$
$59 - 62$ $60.5$ $95$ $3$ $285$
$62 - 65$ $63.5$ $20$ $6$ $120$
$\sum f_{i} = 400$ $\sum f_{i} d_{i} = - 165$
$M e a n (¯ ¯ ¯ x) = A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$

$= 57.5 - \frac{165}{400}$

$= 57.5 - 0.4$
$= 57.1$

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No. of apples	$50 - 53$	$53 - 56$	$56 - 59$	$59 - 62$	$62 - 65$
No of boxes	$20$	$150$	$115$	$95$	$20$

$N o . o f a p p l e s$	$x_{i}$	$f_{i}$	$d_{i} = x_{i} - A$	$f_{i} d_{i}$
$50 - 53$	$51.5$	$20$	$- 6$	$- 120$
$53 - 56$	$54.5$	$150$	$- 3$	$- 450$
$56 - 59$	$57.5 = A$	$115$	$0$	$0$
$59 - 62$	$60.5$	$95$	$3$	$285$
$62 - 65$	$63.5$	$20$	$6$	$120$
		$\sum f_{i} = 400$		$\sum f_{i} d_{i} = - 165$

Find the mean of the following frequency distribution by the assumed mean method :No. of apples50−5353−5656−5959−6262−65No of boxes201501159520

No.ofapples xi fi di=xi−A fidi50−53 51.5 20 −6 −120 53−56 54.5 150 −3 −450 56−5957.5=A115 0 0 59−62 60.5 95 3 285 62−65 63.5 20 6 120 ∑fi=400 ∑fidi=−165 Mean(¯¯¯x)=A+∑fidi∑fi =57.5−165400 =57.5−0.4 =57.1

Find the mean of the following frequency distribution by the assumed mean method :
No. of apples $50 - 53$ $53 - 56$ $56 - 59$ $59 - 62$ $62 - 65$
No of boxes $20$ $150$ $115$ $95$ $20$