Question

The following data for a random sample of banks in two cities represent the ATM fees for using another​ bank's ATM. Compute the range and sample standard deviation for ATM fees for each city. what is the standard deviation for city A? what is the standard deviation for city B? Which city has the most dispersion based on​ range? Which city has more dispersion based on the standard​ deviation? City A 2.5 1.0 1.0 0.0 2.0 City B 1.25 1.00 1.50 1.00 1.00

Answer 1

(A) To find the standard deviation for city A:

From the given data, the following Table is calculated:

n = 5

= 6.5/5 = 1.3

x	x -	(x - )2
2.5	1.2	1.44
1	- 0.3	0.09
1	- 0.3	0.09
0	-1.3	1.69
2	0.7	0.49
Total =		3.8

Standard Deviation (s) is given by:

So,

Standard Deviation for city A = 0.9747

(B)

To find the standard deviation for city B:

From the given data, the following Table is calculated:

n = 5

= 5.75/5 = 1.15

x	x -	(x - )2
1.23	0.1	0.01
1	- 0.15	0.09225
1.5	0.35	0.1225
1	- 0.15	0.0225
1	- 0.15	0.0225
Total =		0.2

Standard Deviation (s) is given by:

So,

Standard Deviation for city B = 0.2236

(C)

Range of City A = Maximum - Minimum = 2.5 - 0 = 2.5

Range of City B = Maximum - Minimum = 1.5 - 1.0 = 0.5

City A has the most dispersion based on range

(D)

City A has the most dispersion based on the standard deviation.