The mean deviation about the mean for the data $3, 10, 10, 4, 7, 10, 5$ is:

Solution

1. First, calculate the mean $\bar{x}$ of the data set: $$\begin{array}{rl}\bar{x}& =\frac{3+10+10+4+7+10+5}{7}\\ & =\frac{49}{7}\\ & =7\end{array}$$.
2. Next, find the absolute deviations from the mean: $$\begin{array}{rl}|3-7|& =4,|10-7|\\ & =3,|10-7|\\ & =3,|4-7|\\ & =3,|7-7|\\ & =0,|10-7|\\ & =3,|5-7|\\ & =2\end{array}$$.
3. Calculate the mean deviation by averaging these absolute values: $\frac{4+3+3+3+0+3+2}{7}=\frac{16}{7}\approx 2.28$.
4. Hence the answer is (B).