Suppose 12

Suppose in a physics test involving 30 students, and four scored 75%, eight scored 60%, twelve scored 50%, and six scored 30%. Calculate the mean of the group and the standard deviation.

Correct answer:

m =  52 %
s =  13.8713

Step-by-step explanation:

$$\begin{gathered} n=30 \\ m=\frac{4\cdot 75+8\cdot 60+12\cdot 50+6\cdot 30}{n}=\frac{4\cdot 75+8\cdot 60+12\cdot 50+6\cdot 30}{30}=52\% \end{gathered}$$

$$\begin{gathered} r=4\cdot (75-m{)}^2+8\cdot (60-m{)}^2+12\cdot (50-m{)}^2+6\cdot (30-m{)}^2=4\cdot (75-52{)}^2+8\cdot (60-52{)}^2+12\cdot (50-52{)}^2+6\cdot (30-52{)}^2=5580 \\ {r}_2=\frac{r}{n-1}=\frac{5580}{30-1}=\frac{5580}{29}=192\frac{12}{29}\doteq 192.4138 \\ s=\sqrt{r_2}=\sqrt{192.4138}=13.8713 \end{gathered}$$

Try another example