If mean of following data is $215$ then find $k$
Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
F $6$ $4$ $3$ $k$ $2$

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Solution

The frequencies are $6, 4, 3, k, 2$
$\sum f_{i} = 6 + 4 + 3 + k + 2 = 15 + k$
$x_{i} = 5, 15, 25, 35, 45$
$x_{i} f_{i} = 30 + 60 + 75 + 35 k + 90 = 255 + 35 k ¯ x = \frac{\sum x_{i} f_{i}}{\sum f_{i}} = \frac{255 + 35 k}{15 + k} = 215 255 + 35 k = 3225 + 15 k 20 k = 2970 k = \frac{2970}{20} = 148.5$

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Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
F	$6$	$4$	$3$	$k$	$2$

If mean of following data is 215 then find kClass0−1010−2020−3030−4040−50F643k2

The frequencies are 6,4,3,k,2∑fi=6+4+3+k+2=15+kxi=5,15,25,35,45xifi=30+60+75+35k+90=255+35k¯x=∑xifi∑fi=255+35k15+k=215255+35k=3225+15k20k=2970k=297020=148.5

If mean of following data is $215$ then find $k$
Class $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
F $6$ $4$ $3$ $k$ $2$