Question

the following scores in their end-of-year math What was the mean deviation of their scores? 23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%, 72%, and 82% A. 14% B. 15% C. 16% D. 17%

Answer 1

First, we need to compute the mean for these 10 values:

$\mu=\frac{23+37+45+49+56+63+63+70+72+82}{10}$

hence,

$\begin{gathered} \mu=\frac{560}{10} \\ \mu=56 \end{gathered}$

Now, we need to find the distance of each value from that mean

$\begin{gathered} \text{Value Distance form 56 } \\ 23\text{ }33 \\ 37\text{ }19 \\ 45\text{ 11} \\ 49\text{ 7} \\ 63\text{ 7} \\ 63\text{ 7} \\ 70\text{ 4} \\ 72\text{ 6} \\ 82\text{ }26 \end{gathered}$

Finally, we must find the mean of those distances:

$\begin{gathered} \operatorname{mean}\text{ deviation=}\frac{33+19+11+3+7+7+4+6+26}{10} \\ \operatorname{mean}\text{ deviation=}\frac{116}{10} \\ \operatorname{mean}\text{ deviation=}11.6 \end{gathered}$