If the S.D. of a variable $X$ is $\sigma $, then the S.D. of $\frac{{a\;X + b}}{c}\left( {a,b,c\;{\rm{are\;constant}}} \right),$ is

JEE MATHEMATICS MCQ: STATISTICS

1 Easy

1 of 1

Application +4 | -1

If the S.D. of a variable

X

\sigma

, then the S.D. of

\frac{{a\;X + b}}{c}\left( {a,b,c\;\mathrm{are\;constant}} \right),

View answer and explanation

Correct option: B

\left| {\frac{a}{c}} \right|\sigma

Option B (

\left| {\frac{a}{c}} \right|\sigma

) is correct because the standard deviation of a linear transformation of a variable is the absolute value of the coefficient times the original standard deviation.

More Questions from STATISTICS

Practice All Chapter MCQs →

If the mean of a set of observations

{x_1},{x_2}, \ldots ,{x_n}

\bar X,

then the mean of the observations

{x_i} + 2\;i;i = 1,\;2, \ldots ,n

is The sum of 10 items is 12 and sum of their squares is 18 , then standard deviation will be In a family, there are 8 men, 7 women and 5 children whose mean ages separately are respectively 24,20 and 6 years. The mean age of the family is The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is

1,3,5, x, y

are 5 observations. Mean of these observations is 5 and variance is 8. Sum of the cubes of the two missing number equals: If s.d. of a set of observations is 8 and if each observation is divided by

-2,

the s.d. of the new set of observations will be