Question

Two hospitals agree to compare the recovery times of patients after they experience a serious fracture for research purposes. They collect data from 10 patients each and compare the number of days stay recorded for each patient Task Compare the recovery time measured as number of days stay in a hospital for Hospital A with Hospital B. How does each hospital compare with the national expected standard? Steps to help answer the question Calculate the five number summary for each sample and display graphically. Excel can be used, but values should be contirmed by hand calculations Use Excel to calculate the mean and standard deviation for each sample. Graph these associated measures so that hospitals can be compared Compare the two samples using all measures calculated above Compare each measure of central tendency with the national expected standard Useful information Table 3.1 Number of days of stay after a serious fracture for Hospital A and Hospital B Hospital A Hospital B 10 10 19 10 20 12 16 20 17 21 18 21 20 21 25 20 25 21 27 25 The national expected standard after a serious fracture, measured as number of days stay, is 20 days .

Answer 1

1)

	A	B
	10	10
	19	10
	20	12
	20	16
	21	17
	21	18
	21	20
	25	20
	25	21
	27	25
minimum	10	10
Q1	20	13
median	21	17.5
Q3	24	20
maximum	27	25

2)

	A	B
mean	20.9	16.9
sd	4.653553	4.976612

20 15 10 0 mean sd

3)

We see that Hospital A has larger mean than that of Hospital B

Standard deviation of A is less than that of Hospital B

Formulas in Excel

	A	B
	10	10
	19	10
	20	12
	20	16
	21	17
	21	18
	21	20
	25	20
	25	21
	27	25
minimum	=MIN(B2:B11)	=MIN(C2:C11)
Q1	=QUARTILE(B2:B11,1)	=QUARTILE(C2:C11,1)
median	=QUARTILE(B2:B11,2)	=QUARTILE(C2:C11,2)
Q3	=QUARTILE(B2:B11,3)	=QUARTILE(C2:C11,3)
maximum	=MAX(B2:B11)	=MAX(C2:C11)
	A	B
mean	=AVERAGE(B2:B11)	=AVERAGE(C2:C11)
sd	=STDEV(B2:B11)	=STDEV(C2:C11)