A sample of customers from Barnsboro National Bank shows an average account balance of $315 with a standard deviation of $87. A sample of customers from Wellington Savings and Loan shows an average account balance of $8350 with a standard deviation of $1800. Which statement about account balances is correct? (A)Barnsboro Bank has more variation. (B)Wellington S&L has more variation. (C)Both have the same variation.

Respuesta :

Answer:

(A)Barnsboro Bank has more variation.

Step-by-step explanation:

The coefficient of variation of a set is given by the following formula

[tex]CV = \frac{S}{M}[/tex]

In which M is the mean and S is the standard deviation.

The higher the coefficient, the higher the variation of the set.

Barnsboro National Bank

[tex]M = 315, S = 87[/tex]

So

[tex]CV = \frac{S}{M} = \frac{87}{315} = 0.276[/tex]

Wellington S&L

[tex]M = 8350, S = 1800[/tex]

So

[tex]CV = \frac{S}{M} = \frac{1800}{8350} = 0.216[/tex]

The Barnsboro National Bank has the highest coefficient, so it has more variation.

The correct answer is:

(A)Barnsboro Bank has more variation.