The mean of four observations a, b, c, d, is If A = a – 5, B = b -10, C = c -25 and D = d – 40, then mean of A, B, C, D is

The correct answer is (a).

The mean of four observations $a$, $b$, $c$, and $d$ is $\frac{a+b+c+d}{4}$. If $A=a-5$, $B=b-10$, $C=c-25$, and $D=d-40$, then the mean of $A$, $B$, $C$, and $D$ is

$$\frac{A+B+C+D}{4} = \frac{a-5+b-10+c-25+d-40}{4} = \frac{a+b+c+d-50}{4} = \frac{1}{4}(a+b+c+d) – \frac{50}{4} = \frac{a+b+c+d}{4} – 12.5 = \boxed{10}.$$

Option (b) is incorrect because $25$ is the mean of $A$, $B$, $C$, and $D$ only if $a=b=c=d=25$. Option (c) is incorrect because $30$ is the mean of $A$, $B$, $C$, and $D$ only if $a=b=c=d=30$. Option (d) is incorrect because $50$ is the mean of $A$, $B$, $C$, and $D$ only if $a=b=c=d=50$.