Community Medicine- Biostatics

1) The diastolic blood pressure of 10 individuals were, 83, 75, 81, 99, 71, 90, 75, 95, 77, 84. Calculate the


a) Range b) standard deviation. What is the significance of calculating SD.






Solution :


a) Range : It is defined as the difference between highest and the lowest figures in a given sample.


In the given sample, highest no is 99


Lowest no. is 71


 Range is 71 to 99 or 99 – 71 = 28


Range is not of much practical significant, because it indicates only the extreme values between the two values and nothing about the dispersion of values between the 2 extreme values.






b) Standard deviation :


It is defined as “Root-means-square-deviation. It is devoted by the Greek letter sigma, ‘’ or S.D.






Formula SD =


Steps :


1) Take deviation of each value from arithmetic mean, ( x – x )


2) Square each deviation, ( x – x )2


3) Add up the squared deviations,  ( x – x )2


4) Divide the result by the number of observations n / (n-1)


5) Then take the square root, which gives the S.D.






x (x – x )


( x – x )2




83 0 0




75 - 8 64


81 - 2 4




99 16 256




71 - 12 144




90 7 49




75 - 8 64




95 12 144


77 - 6 36


84 1 1


830  (x – x )2 = 762






x =






n =(10-1)


Significance of SD :


1) It is an abstract number.


2) It gives us an idea of the ‘spread’ of the dispersion.


3) The larger the SD, the greater the dispersion of values about the mean.






















2) The marks obtained by the students at the extreme examination were as follows.


24 35 38 23


26 33 36 20


34 38 42 38


Calculate the SD and coefficient of variation.






Solution :


a) Standard deviation :






x (x – x )


( x – x )2




24 - 8 64


26 - 6 36


34 2 4


35 3 9


33 1 1


38 6 36


38 6 36


36 4 16


42 10 100


23 - 9 81


20 - 12 144




38 6 36


387 536






n =12






x =  32


b) Coefficient of variation : It is the SD expressed as percentage of mean






CV =














= 22.34%










3) A school health survey was carried out in rural and urban schools, to examine vitamin A deficiency among the students.


The results are given in the table.


School No: of students examined No: of students with vit A deficiency


Urban 100 12


Rural 125 25


Examine whether the proportion of vitamin A deficiency is significantly different in rural and urban schools.






Solution:


As the sample size is > 30; Z test to be applied.


Significantly different  Difference in proportions to be applied.






Proportion of students with vitamin A deficiency =


= 12%






Proportion of students with vitamin A deficiency =


= 20%


















FORMULA :














P1 = 12%; q1 = 100 – 12 = 88% ; p2 = 20% ; q2 = 100 – 20% = 80% . Applying the formula;






Z =














Z =










= =


If calculated Z value >2 0  significant. Are the calculated Z value is 1.67 ; <2. Hence there is no significant difference in the proportion of vitamin A deficiency.










4) A double blind controlled study was carried out with a new drug A ; and standard drug B and the results are given in the table. The drugs A and B were administered to reduce blood pressure in patients suffering from hypertensions.


Drug Mean reduction in BP (MM Hg) SD (mm Hg) Number of patients


A 15 3 50


B 12 2 50


Can we infer that the new drug is more effective than the standard drug in reducing BP.






Solution:


Applying ‘Z’ test for Means (as SD is given and sample size > 30 in each care A, B).


Formula :






Z = =










Here x1 = 15 ; x2 = 12, n1 = 50, n2 = 50, s1 = 3 ; s2 = 2






Z =






= = = = 0.6










If  calculated Z value is >2  significant. Here the calculated Z value is 0.6 80 there is a significant difference in the effectiveness of the drug in reducing mean blood pressure.


As the mean reduction in BP (mm Hg) for drug A is 15 and drug B is 12, 15 > 12 80 drug A is more effective than A drug B in reducing BP.






5) Following the distribution of STD patients studied in 1997 at C.G hospital , Davangere.


Marital status No: of patients


• Married 84


• Unmarried 99


• Separated 14


• Widowed 3


200


Construct a pie diagram.


Solution:


Number of patients Angle % age


84 x1 a1


99 x2 a2


14 x3 a3


3 x4 a4


200 Total = 360 100










To calculate angle :


200 – 84 x1 = x 84 = 151.2 ; a1 = x 84 = 42


360 – x1


Similarly


x2 = x 99 = 178.2, a2 = x 99 = 49.5






x3 = x 14 = 25.2, a2 = x 14 = 7






x4 = x 3 = 5.4, a2 = x 3 = 1.5














6) Following are the incubation period of 21 Polio Cases :


23, 22, 20, 24, 16, 17, 18, 19, 21, 18, 17, 23, 24, 20, 19, 18, 18, 16, 23, 22, 22.


Calculate Range, Mean, Mean deviation, Std. Deviation.






Solution:


1) Range : 24-16 = 8






2) Mean =






Highest value – Lowest value = 420/ 21 = 20






Mean Deviation :


=






= 49/21 = 2.33






















Std.Deviation =


















Formula :






= = = = 2.65










7) The diastolic BP of 10 individuals was as follows –


83, 75, 81, 79, 71, 55, 75, 84 and 90. find the Range, Std. Deviation and Mean deviation.






Solution:


Range : (Highest – Lowest) Value = 90 – 55 = 35






Mean Deviation ; Mean = ∑






∑x1 – n


= ----------- = 693/9 = 77


n






Mean Deviation = = = 7.11


Formula :






Std. Deviation = = =






= = 10.011 = 10