Correct Answer - Option 3 : The integers are any set of seven consecutive integers
Concept:
Mean (x̅) = Sum of elements/Total number of elements
Standard deviation = \(\rm \sqrt{\frac{\bar x-x_i}{N}}\)
Calculation:
Let, seven consecutive integers be x, x+1, x+2, x+3, x+4, x+5, x+6
Now, mean = \(\rm \frac{x+x+1+x+2+x+3+x+4+x+5+x+6}{7}=\frac{7x+21}{7}\)
= x+3
Now, standard deviation = \(\rm \sqrt{\frac{x+3-x+x+3-x-1 +x+3-x-2 +x+3-x-3 +x+3-x-4 +x+3-x-5 +x+3-x-6}{7}}\)
\(=\rm \sqrt{\frac{28}{7}}\)
\(=\rm \sqrt{4}\)
= 2
Hence, option (3) is correct.