If a constant is added to each value in a given data set to produce a new data set, which one of the following describes how the standard deviation of the new data compares to the standard deviation of the original data set? A. Larger B. Smaller C. Equal to

 C. Equal to

Step-by-step explanation:

The standard deviation is written as:

Sx = √( ∑(xₙ - x)^2/(n-1))

Where xₙ are the values of the data set, n is the number of data points and x is the mean of the data set.

Now, if we add a constant c to all the terms in our data set we will have:

(i will use the ' to denote the transformed data)

xₙ' are now xₙ + c.

And the new mean will be:

x' = ( (x₁ + c) + (x₂ + c) + + (xₙ + c))/n = (c*n + (x₁ + x₂ + ..))/n = c + (x₁ + x₂ +...)/n

x' = c + x

Then the new standard deviation will be:

Sx' =√( ∑(xₙ' - x')^2/(n-1))

Sx' = √( ∑((xₙ+c) - (x +c))^2/(n-1)) = √( ∑(xₙ - x)^2/(n-1)) = Sx

So the standard deviation does not change.

The correct option is C.

step-by-step explanation:

d

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500