Question

if mode =63and median=67 calculate arithmetic mean​

Answer 1

HELLO !

• There is a Empirical Relationship between Mean, Median and Mode i.e :—

3 Median = Mode + 2 Mean

Answer :—

3 (67) = 63 + 2 Mean

201 – 63 = 2 Mean

138 / 2 = Mean

69 = Mean

Therefore, Mean is 69

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Answer 2

$\huge \green \leadsto \rm Question :-$

If Mode = 63, Median = 67, calculate arithmetic mean.

$\huge\green \leadsto \rm Solution:-$

Given, mode = 63

Median = 67

Mean = ?

⭐Let the unknown mean be y.

$\sf \red { 3(Median) - 2(Mean)=Mode}$

$\blue \mapsto \sf 3(67) - 2(y)=63$

$\blue \mapsto \sf 201 - 2y = 63$

$\blue \mapsto \sf -2y=63 - 201$

$\blue \mapsto \sf -y= \Large \frac{-138}{2}$

$\blue \mapsto \sf -y = -69$

$\blue \mapsto \sf y=69$

⭐ Therefore, if Mode = 63, Median = 67, the arithmetic mean = 69.

$\huge \green \leadsto \rm Verification:-$

$\sf \red {3(Median)-2(Mean)=Mode}$

$\blue \mapsto \sf 3(67)-2(69)=63$

$\blue \mapsto \sf 201 - 138 = 63$

$\blue \mapsto \sf 63=63$

⭐LHS = RHS

⭐ Hence, verified !!

_________________________

All done :)

_Sita05☄️