RT Book, Section
A1 Glantz, Stanton A.
SR Print(0)
ID 57421297
T1 Appendix C. Answers to Exercises
T2 Primer of Biostatistics, 7e
YR 2012
FD 2012
PB The McGraw-Hill Companies
PP New York, NY
SN 978-0-07-178150-3
LK accessanesthesiology.mhmedical.com/content.aspx?aid=57421297
RD 2024/02/28
AB 2-1 The mean is the sum of the observations divided by the number of observations, 24: 965/24 = 40.2. To find the median we list the observation in order, then select the (50/100)(24 + 1) = 12.5th point, which is the average of the 12th and 13th observations, (29 + 30)/2 = 29.5. The standard deviation is the square root of the sum of the squared differences between the observations and the sample mean divided by the sample size minus 1, 29.8. The 25th percentile is the (25/100)(24 + 1) = 6.25. Thus, the 25th percentile is between the 6th and 7th observation, which we average to obtain (13 + 13)/2 = 13. Likewise, the 75th percentile is (75/100)(24 + 1) = 18.75, so we average the 18th and 19th observations to obtain (70 + 70)/2 = 70. The fact that the median is very different from the mean (29.5 versus 40.2) and not located roughly equidistant between the top and bottom quartile indicates that the data were probably not drawn from a normal distribution. (If the data were symmetrically distributed about the median, we could have further checked for normality by computing the 2.5th, 16th, 84th and 97.5th percentiles and comparing them with values 2 and 1 standard deviations below and above the mean, as described in Fig. 2-10.)