Below-average 60271

In a given group of numbers, one number is equal to the average of all, the largest number is 7 larger than the average, the smallest is 7 smaller than the average, and most numbers in the group have below-average values.

What is the smallest number of numbers in a group?

Correct answer:

n =  5

Step-by-step explanation:

x1 = 7 +μ x2 = μ  7 cnt( xi < μ )  n/2  μ =  nΣ xi  x2 < μ x1 > μ  n=2, μ = 0 n=3, x3 = μ = 0  μ=1  x1=μ+7=1+7=8 x2=μ7=17=6 x3=(μ 3x1x2)/1=(1 38(6))/1=1 μ3=3x1+x2+x3=38+(6)+1=1  y1=μ+7=1+7=8 y2=μ7=17=6 y3=(μ 4y1y2)/21=(1 48(6))/21=0 y4=(μ 4y1y2y3)/1=(1 48(6)0)/1=2 μ4=4y1+y2+y3+y4=48+(6)+0+2=1 cnt(y<μ) = 2 cnt(yμ) = 1+1  z1=μ+7=1+7=8 z2=μ7=17=6 z3=(μ 5z1z2)/31=(1 58(6))/31=0 z4=z3=0 z5=(μ 5z1z2z3z5)/1=(1 58(6)03)/1=3 μ5=5z1+z2+z3+z4+z5=58+(6)+0+0+3=1 cnt(z<μ) = 3 cnt(zμ) = 1+1  n=5

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