Characteristics: 80608

Arithmetic mean xA=40 and standard deviation sx=8 were calculated. Determine from which numbers the student calculated the given characteristics:
a) 24 and 56
b) 16 and 64
c) 32 and 48

Correct answer:

x = c

Step-by-step explanation:

$$\begin{gathered} n=2 \\ {m}_1=\frac{24+56}{2}=40 \\ {m}_2=\frac{16+64}{2}=40 \\ {m}_3=\frac{32+48}{2}=40 \\ {\sigma }_1=\sqrt{\frac{(24-m_1{)}^2+(56-m_1{)}^2}{n}}=\sqrt{\frac{(24-40{)}^2+(56-40{)}^2}{2}}=16 \\ {\sigma }_2=\sqrt{\frac{(16-m_2{)}^2+(64-m_2{)}^2}{n}}=\sqrt{\frac{(16-40{)}^2+(64-40{)}^2}{2}}=24 \\ {\sigma }_3=\sqrt{\frac{(32-m_3{)}^2+(48-m_3{)}^2}{n}}=\sqrt{\frac{(32-40{)}^2+(48-40{)}^2}{2}}=8 \\ x=c \end{gathered}$$

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