Pharmaceutical Statistics
`
`David S. Jones
`
`BSc, PhD, CEng CChem, FIM, FRSS, MRSC, MPDSNl
`
`Professor of Biomaterials Science
`
`School of Pharmacy
`
`Queen’s University of Belfast
`Belfast, UK
`
`(RP
`
`Landon - Chicago Pharmaceutical Press
`Mylan v. MonoSol
`Mylan V. MonoSol
`IPR2017-00200
`IPR2017-00200
`MonoSol Ex. 2031
`MonoSol Ex. 2031
`Page 1
`Page 1
`
`

`

`Published by the Pharmaceutical Press
`Publications division of the Royal Pharmaceutical Society of Great Britain
`
`1 Lombelh High Street, London SE1 7JN, UK
`100 30th Atkinson Road, Suite 206, Grayslcrker IL 60030-7820, USA
`
`© Pharmaceutical Press 2002
`
`First published 2002
`
`Text design by Barker/Hilsdon, Lyme Regis, Dorset
`Typeset by MCS Ltd, Salisbury, Wiltshire
`Printed in Great Britain by T] International, Padstow, Cornwall
`
`ISBN_0 85369 425 7
`
`All rights reserved. No part of this publication may be reproduced,
`stored in a retrieval system, or transmitted in any form or by any
`means, without the prior written permission of the copyright holder.
`
`The publisher makes no representation, express or implied, with
`regard to the accuracy of the information contained in this book and
`cannot accept any legal responsibility or liability for any errors or
`omissions that may be made.
`
`A catalogue record for this book is available from the British Library
`
`
`
`
`
`Page 2
`Page 2
`
`

`

`24 Measurement of central tendency and variation of data
`
`and should be recalled whenever the reader is checking calculations. If
`Such an approximate relationship is not observed, then it is strongly
`advised that all the calculations shOuld be re-checked.
`
`2.2.4.1 General comments on the standard deviation
`
`The standard deviation is the most commonly used measure of the dis-
`persion of data, because it may be related to the probability of a meas-
`urement occurring within certain regions on the frequency distribution.
`Thus,
`in normal
`(symmetrical), and indeed in moderately skewed
`(asymmetrical) distributions:
`
`I
`
`0
`
`0
`
`68.27% of all values are included within the numerical range described by X
`+ s and X M 5, namely one standard deviation around the mean.
`95.45% of all values are included within the numerical range described by X
`+ 25 and X — 23, namely two standard deviations around the mean.
`99.73 % of all values are included within the numerical range described by X
`+ 33 and X - 35, namely three standard deviations around the mean.
`
`In the example described above concerning the time required for the
`release of 50% of the original loading of therapeutic agents, the mean and
`standard deviation were calculated to be 23.6 i 2.3 h. Consequently
`
`‘-
`
`0
`
`.
`
`68.27% of all values are included within the numerical range described by
`
`21.3 h (i.e. 23.6 —2.3 h) to 25.9 h (i.e. 23.6 + 2.3 h).
`Therefore, in the current example, 10 out of 15 values were distributed with-
`
`in this range.
`95.45% of all values are included within the numerical range described by
`
`19.0 h (i.e. 23.6 — 4.6 h) to 28.2 h (i.e. 23.6 + 4.611).
`Therefore, in the current example, 14 out of 15 values were distributed with-
`
`in this range.
`99.73% of all values are included within the numerical range described by
`
`16.7 h (i.e. 23.6 — 6.9 h) to 30.5 h (i.e. 23.6 + 6.911).
`Therefore, in the current example, all values were distributed within this range.
`
`The standard deviation (and indeed the variance) is dramatically affect—
`ed by extreme values in a population, a point that should be considered
`whenever the variation of a set of data is under discussion. The effects
`of extreme values on the variance is
`illustrated in the following
`
`example.
`
`EXAMPLE 2 . 9 The concentrations (mg/5 mL) 03%; penicillin antibiotic
`in five separate bottles of a paediatric suspension have been examined
`using an iodometric technique. Calculate the mean and standard devia»
`tion and consider the contribution of each observation to the sample
`
`variance.
`
`Page 3
`Page 3
`
`