Increase the mean

To which number should the number 4 be changed between the numbers 4,5,7, 1,0,9,7,8, -3,5 to increase these numbers' arithmetic mean by 1.25?

Correct answer:

x =  16.5

Step-by-step explanation:

$$\begin{gathered} 4,5,7,1,0,9,7,8,-3,5 \\ n=10 \\ s=4+5+7+1+0+9+7+8+(-3)+5=43 \\ {\mu }_1=s\mathrm{/}n=43\mathrm{/}10={\displaystyle \frac{43}{10}}=4\frac{3}{10}=4.3 \\ {\mu }_2={\mu }_1+1.25=4.3+1.25={\displaystyle \frac{111}{20}}=5\frac{11}{20}=5.55 \\ {\mu }_2=s_2\mathrm{/}n \\ n\cdot {\mu }_2=s-4+x \\ x=n\cdot {\mu }_2-s+4=10\cdot 5.55-43+4={\displaystyle \frac{33}{2}}=16\frac{1}{2}=16.5 \end{gathered}$$

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