# Statistics: nth percentile

• Feb 1st 2009, 02:11 AM
angel.white
Statistics: nth percentile
Hi, MHF :) I'm taking stats this semester, and my answer differs from my book's.

I am using software called R (The R Project for Statistical Computing)
My book uses software called Minitab (Statistical Analysis: Data Analysis and Statistics Software and Training | Minitab)

I have two sets of data, one for a group with a high dose of some medicine, and one for the control group:

High = 16.1 , 134.9 , 52.7 , 14.4 , 124.3 , 99.0 , 24.3 , 16.3 , 15.2 , 47.7 , 12.9 , 72.7 , 126.7 , 46.4 , 60.3 , 23.5 , 43.6 , 79.4 , 38.0 , 58.2 , 26.5 , 25.1

Control = 297.1 , 491.8 , 1332.9 , 1172.0 , 1482.7 , 335.4 , 528.9 , 24.1 , 545.2 , 92.9 , 337.1 , 102.3 , 255.1 , 100.5 , 159.9 , 168.0 , 95.2 , 132.5 , 442.6 , 15.8 , 175.6 , 131.1

I need to find for each group:
a) sample mean, variance, and standard deviation
b) sample upper and lower quartiles
c) sample median
d) construct a boxplot
e) 5th and 95th percentiles.

Here are my answers, green implies they agree with the book. Red implies they disagree, and the book's answer will be adjacent.

High Dose:
Sample mean: 52.65
Sample variance: 1490.315
Sample standard deviation: 38.6046 (not given in the book)
Upper Quartile: 69.60 (book: 74.38)
Lower Quartile: 23.70 (book: 21.70)
Sample median: 45.00
5th percentile: .05(22+1) = 1.15 || 1st = 12.9 || 2nd = 14.4 || (12.9+14.4)/2 = 13.65 (book: 13.125)
95th percentile: .95(22+1) = 21.85 || 21st = 126.7 || 22nd = 134.9 || (126.7+134.9)/2 = 80.8 (book: 133.67)

Control:
Sample mean: 382.7
Sample variance: 175224.4
Sample standard deviation: 418.5981 (not given in book)
Upper Quartile: 479.5 (book: 501.1)
Lower Quartile: 109.5 (book: 101.9)
Sample median: 215.3 (book: 215.4 -- probably different rounding rules in our software)
5th percentile: .05(22+1) = 1.15 || 1st = 15.8 || 2nd = 24.1 || (15.8+24.1)/2 = 19.95 (book: 17.045)
95th percentile: .95(22+1) = 21.85 || 21st = 1332.9 || 22nd = 1482.7 || (1332.9+1482.7)/2 = 1407.8 (book: 1460.23)

Can anyone help me figure out why my answers are incorrect?
Thank you.
• Feb 1st 2009, 06:19 AM
ramvenk
Hi I attached word file containing Formulae used in Minitab and calculations of percentiles and Boxplots. Remaining values are given as Minitab output.
Verify their validity using the above given formulae, hope this helps you.