# Jade invested in the stock market. The weekly change in the value of her stock, in dollars, over 4 weeks was +23.65, -22.20, -12.75, and +5.98. What is the average weekly change in the value of her stock, in dollars?

May 19, 2018

There is a trap in this question.

mean change $= \frac{- 45.85 + 9.45 + 18.73}{3} = - 5.89$

#### Explanation:

There are 3 types of average; mean, median and mode. I am assuming you intend the mean to be used.

A mean is that single value which if it is multiplied by the total count of related values it give the same answer as the sum of those related values.

$\textcolor{b r o w n}{\text{This part is the trap in the question}}$

The sum $\to 23.65 - 22.20 - 12.75 + 5.98 = - 5.32$

Count $\to 4$

Mean $\to - \frac{5.32}{4} = 1.33$
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$\textcolor{b r o w n}{\text{Read the question again. This is what it is asking for}}$

$\textcolor{g r e e n}{\text{What is the average weekly "color(red)("change")" in value}}$

$\textcolor{b l u e}{\text{First change }} \to + 23.65 - \left(- 22.20\right) = 45.85$
$\textcolor{w h i t e}{\text{dddddddddddddd}}$but it decreased so the change is negative.

$\textcolor{w h i t e}{\text{dddddddddddddd}} \textcolor{b l u e}{- 45.85}$.
...........................................................................................
$\textcolor{b l u e}{S \text{econd change}} \to - 22.20 - \left(- 12.75\right) = - 9.45$

$\textcolor{w h i t e}{\text{ddddddddddddddd}}$but $- 12.75 > - 22.20$ so it increased
$\textcolor{w h i t e}{\text{ddddddddddddddd}}$thus the change is positive

$\textcolor{w h i t e}{\text{ddddddddddddddd}} \textcolor{b l u e}{+ 9.45}$
...................................................................................................
$\textcolor{b l u e}{\text{Third change}} \to - 12.75 - \left(+ 5.98\right) = - 18.73$
$\textcolor{w h i t e}{\text{dddddddddddddd}}$but it increased thus the change is positive.

$\textcolor{w h i t e}{\text{dddddddddddddd}} \textcolor{b l u e}{+ 18.73}$
.................................................................................................

$\textcolor{b l u e}{\text{Putting it all together}}$

mean change $= \frac{- 45.85 + 9.45 + 18.73}{3} = - 5.89$