Question

A student’s grades in the laboratory, lecture, recitation parts of a course were 71,

78, and 89 respectively.

a. If the weights accorded these grades are 2,4, and 5 respectively, what is an

appropriate average grade?

b. What is the average grade if equal weights are used?​

Answer 1

$\underline{\textsf{Given:}}$

$\begin{array}{|c|c|c|c|}\cline{1-4}\textsf{Grades}&71&78&90\\\cline{1-4}\textsf{Weights}&2&4&5\\\cline{1-4}\end{array}\right)}$

$\underline{\textsf{To find:}}$

$\textsf{a.Weighted average grade}$

$\textsf{b.Average grade if equal weights are used}$

$\underline{\textsf{Solution:}}$

$\textsf{We know that,}$

$\boxed{\textsf{Weighted average}\mathsf{=\dfrac{\sum\,w_i\,x_i}{\sum\,w_i}}}$

$\implies\mathsf{Weighted\;average}\mathsf{=\dfrac{2{\times}71+4{\times}78+5{\times}89}{2+4+5}}$

$\implies\mathsf{Weighted\;average}\mathsf{=\dfrac{142+312+445}{11}}$

$\implies\mathsf{Weighted\;average}\mathsf{=\dfrac{899}{11}}$

$\implies\mathsf{Weighted\;average\,grade=81.72}}$

$\textsf{When equal weights are used, let it be k}$

$\mathsf{Weighted\;average=\dfrac{k{\times}71+k{\times}78+k{\times}89}{k+k+k}}$

$\mathsf{Weighted\;average=\dfrac{71k+78k+89k}{3k}}$

$\mathsf{Weighted\;average=\dfrac{238k}{3k}}$

$\mathsf{Weighted\;average=\dfrac{238}{3}}$

$\implies\boxed{\mathsf{Weighted\;average=79.33}}$

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