The marks obtained by $20$ students in maths are $35, 40, 78, 30, 50, 78, 36, 65, 78, 40, 30, 65, 50, 35, 80, 95, 80, 36, 95, 35$ . Find the Arithmetic mean of the students by direct method.

85.56

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65.86

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56.85

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86.56

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Solution

The correct option is C $56.85$
Arranging in ascending order
$30, 30, 35, 35, 35, 36, 36, 40, 40, 50, 50, 65, 65, 78, 78, 78, 80, 80, 95, 95$ .

$X_{i}$ $F_{i}$ $X_{i} F_{i}$
30 2 60
35 3 105
36 2 72
40 2 80
50 2 100
65 2 130
78 3 156
80 2 160
95 2 190
$Σ F_{i} = 20$ $Σ F_{i} X_{i} = 1131$
Mean = $\frac{Σ F_{i} X_{i}}{Σ F_{i}} = \frac{1131}{20} = 56.55 ≃ 56.85$
C) 56.85

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$X_{i}$	$F_{i}$	$X_{i} F_{i}$
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The marks obtained by 20 students in maths are 35,40,78,30,50,78,36,65,78,40,30,65,50,35,80,95,80,36,95,35. Find the Arithmetic mean of the students by direct method.

The correct option is C 56.85Arranging in ascending order30,30,35,35,35,36,36,40,40,50,50,65,65,78,78,78,80,80,95,95.Xi Fi XiFi 30 2 60 35 3 105 36 2 72 40 280 502 100 65 2 130 78 3 156 80 2160 95 2190 ΣFi=20 ΣFiXi=1131 Mean = ΣFiXiΣFi=113120=56.55≃56.85C) 56.85

The marks obtained by $20$ students in maths are $35, 40, 78, 30, 50, 78, 36, 65, 78, 40, 30, 65, 50, 35, 80, 95, 80, 36, 95, 35$ . Find the Arithmetic mean of the students by direct method.