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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.

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Answer:

The correct option is A as Barnsboro Bank has more variation.

Step-by-step explanation:

From the data

  • 1st sample has a mean of $315 and a standard deviation of $87.
  • 2nd sample has a mean of $8350 and a standard deviation of $1800

Coefficient of Variation for 1st sample is given as

Coefficient of Variation of 1st sample

[tex]\frac{S}{\bar{X}}*100\\\frac{87}{315}*100\\27.62[/tex]

Coefficient of Variation of 2nd sample

[tex]\frac{S}{\bar{X}}*100\\\frac{1800}{8350}*100\\21.56[/tex]

So the coefficient of variation of 1st sample is 27.62 while the coefficient of 2nd sample is 21.56. Thus the 1st sample has more variation thus the second bank.

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