Question

1. determining the mass of an object three times gave the following results: 9.2 g, 9.1 g, and 9.3 g. find the mean mass and the average deviation from the mean.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of data $x_1,x_2,x_3$ is given by $\bar{x}=\frac{x_1 + x_2+x_3}{n}$, where $n = 3$, $x_1=9.2$, $x_2 = 9.1$, $x_3=9.3$.
$\bar{x}=\frac{9.2 + 9.1+9.3}{3}=\frac{27.6}{3}=9.2$ g

Step2: Calculate the deviations

The deviations from the mean are $d_1=x_1-\bar{x}=9.2 - 9.2=0$, $d_2=x_2-\bar{x}=9.1 - 9.2=- 0.1$, $d_3=x_3-\bar{x}=9.3 - 9.2 = 0.1$.

Step3: Calculate the average deviation

The average deviation $AD=\frac{\vert d_1\vert+\vert d_2\vert+\vert d_3\vert}{n}$.
$AD=\frac{\vert0\vert+\vert - 0.1\vert+\vert0.1\vert}{3}=\frac{0 + 0.1+0.1}{3}=\frac{0.2}{3}\approx0.07$ g

Answer:

The mean mass is 9.2 g and the average deviation from the mean is approximately 0.07 g.