Question

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if the mean weight member of a family of 60kg and three of them have the weight 56kg,68kg,and 72kg respectively.Then find the weight of fourth number​

Answer 1

Answer:

62 kg

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Answer 2

Appropriate Question

If the mean weight of the 4 members of a family is 60 kg and three of them have the weight 56 kg,68 kg,and 72 kg respectively. Then find the weight of fourth number.

$\large\underline{\sf{Solution-}}$

Given that,

Mean weight of members of a family = 60 kg

Let assume that

$\rm :\longmapsto\:x_1 = 56 \: kg$

$\rm :\longmapsto\:x_2 = 68 \: kg$

$\rm :\longmapsto\:x_3 = 72 \: kg$

Let assume that weight of the fourth member be

$\rm :\longmapsto\:x_4 = x \: kg$

We know,

Mean for un-grouped data is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ Mean \: = \: \frac{ \sum \: x_i}{n} \: }}}$

where, n is number of observations.

So, on substituting the values, we get

$\rm :\longmapsto\:60 = \dfrac{56 + 68 + 72 + x}{4}$

$\rm :\longmapsto\:60 = \dfrac{196 + x}{4}$

$\rm :\longmapsto\:196 + x = 240$

$\rm :\longmapsto\: x = 240 - 196$

$\rm\implies \:x = 44 \: kg$

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MORE TO KNOW

1. If each observation is increased by some constant k, the mean is increased by same constant k.

2. If each observation is decreased by some constant k, the mean is decreased by same constant k.

3. If each observation is multiplied by some constant k, the mean is multiplied by same constant k.

4. The sum of deviations taken from mean is 0.