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

Average birthweight of infants is approximately 3136 gr. Arithmetic Mean

Ordered data are: Median

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

Multiple modes exist. Mode

The difference between 15th and 16th observations is /4=13.5  Q 1 = = We add 13.5 to 15th observation to find Q1

 Q 3 = = 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

Average distance of observations from the mean is 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= =3402 #of classes=8 Class Int.=3402/8=  426 To find lower limits: = = =4570 To find upper limits: = = = =4995 Lower-upper limit

Mean or

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

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

25=x x=? x X X=2594,3

75=x 1 x=? X

P 75 =Q 3 = % of observations lie below X

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

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

Standart deviation

or

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

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 % Normal Obese Total

Distribution of CHD according to body weight status

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:

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

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

Histogram of T4 values in hypothyroid group

Box plot of T4 values in three groups

Error bars of T4 values in three groups

Scatter plot of T4 values in three groups