First, we start by calculating the numbers after performing the operation described: multiply each number by -1 and add 1 . Let's denote the original numbers as n=1,2,3,...,10. For each (and any) number n :
x=−n+1 Let's apply this operation to each of the first 10 natural numbers: ‌x1=−1+1=0 ‌x2=−2+1=−1 ‌x3=−3+1=−2 ‌x4=−4+1=−3 ‌x5=−5+1=−4 ‌x6=−6+1=−5 ‌x7=−7+1=−6 ‌x8=−8+1=−7 ‌x9=−9+1=−8 ‌x10=−10+1=−9 Next, we calculate the mean (µ) of these obtained values (x1,x2,...,x10) :
‌µ=‌
x1+x2+...+x10
10
=‌
0−1−2−3−4−5−6−7−8−9
10
‌µ=‌
−45
10
=−4.5 Now let's find the variance, which is given by the formula: Variance =‌