Question

the following data for a random sample of banks in two cities represent the atm fees for using another banks atm. compute the sample variance for atm fees for each city.
city a 1.25 1.00 1.50 1.50 1.00
city b 2.00 1.00 1.50 0.00 1.75

the variance for city a is $\square$.
(round to the nearest cent as needed.)

Explanation:

Step1: Calculate sample mean of City A

First, sum the values: $1.25 + 1.00 + 1.50 + 1.50 + 1.00 = 6.25$
Then divide by sample size $n=5$:
$\bar{x}_A = \frac{6.25}{5} = 1.25$

Step2: Compute squared deviations

For each value, calculate $(x_i - \bar{x}_A)^2$:

• $(1.25 - 1.25)^2 = 0$
• $(1.00 - 1.25)^2 = 0.0625$
• $(1.50 - 1.25)^2 = 0.0625$
• $(1.50 - 1.25)^2 = 0.0625$
• $(1.00 - 1.25)^2 = 0.0625$

Step3: Sum squared deviations

Add the squared deviations:
$0 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.25$

Step4: Calculate sample variance

Divide sum by $n-1=4$ (sample variance uses $n-1$):
$s_A^2 = \frac{0.25}{4} = 0.0625$

Step5: Round to nearest cent

Round $0.0625$ to two decimal places: $0.06$

Answer:

0.06