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:

4,5,7,1,0,9,7,8,−3,5 n=10 s=4+5+7+1+0+9+7+8+(−3)+5=43 μ1=s/n=43/10=4310=4310=4.3 μ2=μ1+1.25=4.3+1.25=11120=51120=5.55  μ2=s2/n n⋅ μ2=s−4+x  x=n⋅ μ2−s+4=10⋅ 5.55−43+4=16.5

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