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Practice. Descriptive statistics Tables Graphs. Birthweights of 60 infants are given below:. Find Mean, median and mode Q 1 , Q 3 Standard deviation and coefficient of variation. Arithmetic Mean. Average birthweight of infants is approximately 3136 gr. Median. Ordered data are:.

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**Practice**Descriptive statistics Tables Graphs**Find**• Mean, median and mode • Q1, Q3 • Standard deviation and coefficient of variation**Arithmetic Mean**Average birthweight of infants is approximately 3136 gr.**Median**Ordered data are:**31st value**30th value n=60 Median is 3110**Mode**Multiple modes exist.**The difference between 15th and 16th observations is 54.**54/4=13.5 We add 13.5 to 15th observation to find Q1 Q1=2540+13.5=2553.5**The difference between 45th and 46th observations is 90.**3*(90/4)=67.5 We add 67.5 to 45th observation to find Q3 Q3=3610+67.5=3677.5**Average distance of observations from the mean is 754.37 gr.****If infant weight were given as kg instead of gr, what would**be the result of the mean and standart deviation. Find the result without using any formulations.**The amount variation between observations in this**distribution is 24% in terms of the mean.**L=1588**H=4990 Range=H-L=4990-1588=3402 #of classes=8 Class Int.=3402/8=425.25426 To find lower limits: 1588 1588+426=2014 2014+426=2440 . . . 4114+426=4570 To find upper limits: 2014-1=2013 2013+426=2439 2439+426=2865 . . . 4569+426=4995 Lower-upper limit 1588-2013 2014-2439 2440-2865 . . . 4570-4995**Mean**or**Median**Since the class midpoint of interval which has the largest frequency is 3078.5, mode is 3078.5**Measures of position**What are the 25th, 75th percentiles and the median?**2439.5 18.33**X 25 2865.5 36.67 x=? 25=x1 X=2594,3 36.67-18.33 2865.5-2439.5 25-18.33 x-2439.5**75=x1**x=? 3291.5 60.0 X 75 3717.5 78.33**3291.5 60.0**X 75 3717.5 78.33 P75=Q3=3640.1 75% of observations lie below 3640.1.**90%**Normal b.w 5% 5% x1 x2 If the central %90 were considered as normal birthweight, what are the two limits for normality?**90%**Normal b.w 5% 5% x1 x2 . . . . . . . . . x2 95 x1**Coefficient of variation**The amount variation between observations in this distribution is 23.4% in terms of the mean.**Body weight status**CHD Total Yes No n % n % Normal 4 8 46 92 50 Obese 10 25 30 75 40 Total 14 16 76 84 90 A study wasconducted to analyze the relation between coronary heart disease (CHD) and body weight status (obese and normal). Observed values are as follows:**Example**• In a goiter hyper-endemic area, thyroid gland and its hormones T3, T4 and TSH (Thyroid Stimulating Hormone) were studied in 225 subjects in three groups • Hypothyroid • Euthyroid • Hyperthyroid • T4 levels of three study groups are observed as follows:**GROUPS**Hypothyroid Euthyroid Hyperthyroid Mean 2,46 6,38 13,16 Median 2,40 6,10 13,20 Mode 3,40 4,80 12,1 & 14,2 Std. Deviation 0 ,82 2,37 2,14 Variance 0 ,68 5,62 4,58 C V 33,33 37, 15 16,26 Minimum 1,10 1,60 9,40 Maximum 4,00 12,50 18,10 Range 2,90 10,90 8,70 Descriptive Statistics of the study groups for T4 Quartiles 1st (25%) 1,70 4,80 11,30 3rd (75%) 3,10 8,10 14,70**Classification of the T4 values in hypothyroid group**Min = 1,1 Max = 4,0 Range = 4,0 – 1,1 = 2,9 # of classes = 8 Class Int. = 2,9/8 = 0,36 0,4

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