In a scientific experiment, the mass of an object was determined to be 20.450 g, 20.313 g, and 21.013 g. What is the mean mass of the object? And the average deviation from the mean?

Aug 25, 2017

$\text{Mean} = 20.592$ $\text{g}$

$\text{Mean deviation} = 0.281$ $\text{g}$

Explanation:

The "mean" of a certain set of numbers is the average value across all the numbers.

To find the mean, we must add the numbers, and then divide the result by how many numbers we added.

In this case, there are three numbers, so we divide the result by $3$.

Let's calculate the mean mass:

Rightarrow "Mean" = frac(20.450 " g" + 20.313 " g" + 21.013 " g")(3)

Rightarrow "Mean" = frac(61.776 " g")(3)

$\therefore \text{Mean} = 20.592$ $\text{g}$

Then, let's find the distance $\sigma$, or "deviation", between each mass value and the mean.

Remember, the distance should not be negative, so we will find the absolute value of each distance:

$R i g h t a r r o w {\sigma}_{1} = | 20.450$ $\text{g}$ $-$ $20.592$ $\text{g}$ $| = | - 0.142$ $\text{g}$ $| = 0.142$ $\text{g}$

$R i g h t a r r o w {\sigma}_{2} = | 20.313$ $\text{g}$ $-$ $20.592$ $\text{g}$ $| = | - 0.279$ $\text{g}$ $| = 0.279$ $\text{g}$

$R i g h t a r r o w {\sigma}_{3} = | 21.013$ $\text{g}$ $-$ $20.592$ $\text{g}$ $| = | 0.421$ $\text{g}$ $| = 0.421$ $\text{g}$

The mean of these distances will be the average deviation from the mean.

It is more simply known as the "mean deviation":

Rightarrow "Mean deviation" = frac(0.142 " g" + 0.279 " g" + 0.421 " g")(3)

Rightarrow "Mean deviation" = frac(0.842 " g")(3)

$R i g h t a r r o w \text{Mean deviation} = 0.2806666667$ $\text{g}$

$\therefore \text{Mean deviation} \approx 0.281$ $\text{g}$