My Question:In a shopping basket are six items that have

Berikut ini adalah pertanyaan dari MomentsOfAlwaysness pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

My Question:In a shopping basket are six items that have a mean price of $17.50. Five of the items cost $18, $22, $13, $9 and $36. How much did the sixth item cost?

Your's Answer: ?

Jawaban dan Penjelasan

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The sixth item cost $7.

Explanation

Mean Value

Question
In a shopping basket, there are six items that have a mean price of $17.50. Five of them cost $18, $22, $13, $9 and $36. How much did the sixth item cost?

Solution
The mean value of $n$ data ( $\bar{x}$ ) is calculated using this formula:

$\large\text{$\begin{aligned}\bar{x}&=\frac{\displaystyle\sum_{i=1}^{n}x_i}{n}\\&=\frac{x_1+x_2+{\dots}+x_n}{n}\end{aligned}$}$

Thus,

$\begin{aligned}\bar{x}&=\frac{x_1+x_2+{\dots}+x_6}{6}\\\Rightarrow 6\bar{x}&=x_1+x_2+{\dots}+x_6\\\Rightarrow\;\!x_6&=6\bar{x}-(x_1+x_2+{\dots}+x_5)\end{aligned}$

Solving it by substituting the mean value and known prices:

$\begin{aligned}x_6&=6\bar{x}-(x_1+x_2+{\dots}+x_5)\\&=6\cdot\$17.50-(\$18+\$22+\$13+\$9+\$36)\\&=\$105-\$98\\\therefore\ x_6&=\boxed{\ \bf\$7\ }\end{aligned}$