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Practice Descriptive statistics Tables Graphs

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Birthweights of 60 infants are given below:

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Find Mean, median and mode Q 1, Q 3 Standard deviation and coefficient of variation

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Average birthweight of infants is approximately 3136 gr. Arithmetic Mean

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Ordered data are: Median

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30th value 31st value n=60 Median is 3110

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Multiple modes exist. Mode

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The difference between 15th and 16th observations is 54. 54/4=13.5 Q 1 =2540+13.5=2553.5 We add 13.5 to 15th observation to find Q1

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Q 3 =3610+67.5=3677.5 The difference between 45th and 46th observations is 90. 3*(90/4)=67.5 We add 67.5 to 45th observation to find Q 3

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Average distance of observations from the mean is 754.37 gr.

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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.

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The amount variation between observations in this distribution is 24% in terms of the mean.

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L=1588 H=4990 Range=H-L=4990-1588=3402 #of classes=8 Class Int.=3402/8=425.25 426 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

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Mean or

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Median Since the class midpoint of interval which has the largest frequency is 3078.5, mode is 3078.5

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Measures of position What are the 25 th, 75 th percentiles and the median?

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25=x 1 36.67-18.33 25-18.33 x=? x-2439.5 2865.5-2439.5 2439.5 18.33 X 25 2865.5 36.67 X=2594,3

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75=x 1 x=? 3291.5 60.0 X 75 3717.5 78.33

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P 75 =Q 3 =3640.1 75% of observations lie below 3640.1. 3291.5 60.0 X 75 3717.5 78.33

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If the central %90 were considered as normal birthweight, what are the two limits for normality? x1x1 x2x2 Normal b.w 90% 5%

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.................. x1x1 x2x2 Normal b.w 90% 5% x1x1 95 x2x2

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Standart deviation

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or

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Coefficient of variation The amount variation between observations in this distribution is 23.4% in terms of the mean.

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A study was conducted to analyze the relation between coronary heart disease (CHD) and body weight status (obese and normal). Observed values are as follows: Body weight status CHD Total YesNo n%n % Normal48469250 Obese1025307540 Total1416768490

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Distribution of CHD according to body weight status

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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:

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T4 levels of the study groups Hypothyroid Group 1,11,72,12,73,4 1,11,72,12,73,4 1,11,72,12,83,4 1,11,72,42,93,4 1,11,92,42,93,4 1,21,92,42,93,4 1,22,02,42,93,4 1,42,02,42,93,5 1,52,02,53,03,5 1,52,02,53,13,7 1,52,02,53,13,7 1,52,02,63,13,9 1,52,02,63,43,9 1,62,12,73,43,9 1,62,12,73,44,0 Euthyroid Group 1,64,55,56,98,4 2,14,85,67,18,6 2,44,85,77,18,6 2,44,85,77,18,7 2,84,86,07,19,6 3,04,86,17,29,6 3,04,96,17,59,6 3,45,06,17,69,6 3,45,06,48,09,7 3,85,06,48,09,9 4,05,16,48,19,9 4,05,16,68,110,4 4,25,16,78,110,9 4,25,56,78,411,4 4,35,56,98,412,5 Hyperthyroid Group 9,411,212,413,915,0 9,411,212,613,915,0 9,511,212,714,015,0 9,611,312,714,215,1 10,011,812,714,215,6 10,011,813,014,215,6 10,011,813,214,216,2 10,312,013,214,216,3 10,312,113,414,416,4 10,312,113,514,616,7 10,912,113,514,716,7 11,012,113,514,716,7 11,012,113,514,716,7 11,012,413,614,817,9 11,212,413,614,818,1

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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

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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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Histogram of T4 values in hypothyroid group

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Box plot of T4 values in three groups

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Error bars of T4 values in three groups

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Scatter plot of T4 values in three groups

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