Question

Find x and y if the mean is 62.8 and sum of frequencies=50
Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100
Frequency 5
х
10
у
7
100-120
8​

Answer 1

$Given \: \sum f_{i} = 50$

$\implies 30 + x + y = 50$

$\implies x = 50 - 30 - y$

$\implies x = 20 - y \: --(1)$

$Mean = 62.8 \: (given)$

$\implies \frac{ \sum f_{i}x_{i}}{\sum f_{i} } = 62.8$

$\implies \frac{2060+30x+70y}{50} = 62.8$

$\implies 2060+30x+70y = 50 \times 62.8$

$\implies 2060+30(20-y)+70y = 3140$

$\implies 2060+600-30y+70y = 3140$

$\implies 2660+40y = 3140$

$\implies 40y = 3140 - 2660$

$\implies 40y = 480$

$\implies y = \frac{480}{40}$

$\implies y = 12\: --(2)$

$Put \: y = 12 \: in \: equation \: (1), we \:get$

$\implies x = 20 - 12$

$\implies x = 8$

Therefore.,

$\red{ Value \:of \:x } \green { = 8 }$

$\red{ Value \:of \:y } \green { = 12 }$

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