Practice

1
Practice

• Descriptive statistics
• Tables
• Graphs

2
Birthweights of 60 infants are given below
3

• Find
• Mean, median and mode
• Q1, Q3
• Standard deviation and coefficient of variation

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Arithmetic Mean
Average birthweight of infants is approximately
3136 gr.
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Median
Ordered data are
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n60
Median is 3110
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Mode
Multiple modes exist.
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(No Transcript)
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The difference between 15th and 16th observations
is 54.
54/413.5
We add 13.5 to 15th observation to find Q1
? Q1254013.52553.5
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(No Transcript)
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The difference between 45th and 46th observations
is 90.
3(90/4)67.5
We add 67.5 to 45th observation to find Q3
? Q3361067.53677.5
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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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L1588 H4990
? RangeH-L4990-15883402
of classes8 Class Int.3402/8425.25?426
To find lower limits 1588 15884262014 2014426
2440 . . . 41144264570
To find upper limits 2014-12013 20134262439 24
394262865 . . . 45694264995
Lower-upper limit 1588-2013 2014-2439
2440-2865 . . .
4570-4995
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(No Transcript)
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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 25th, 75th percentiles and the
median?
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(No Transcript)
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2439.5
18.33 X
25 2865.5
36.67
36.67-18.33
25-18.33
2865.5-2439.5
x-2439.5
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3291.5 60.0 X 75
3717.5 78.33
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3291.5 60.0 X 75
3717.5 78.33
P75Q33640.1
75 of observations lie below 3640.1.
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If the central 90 were considered as normal
birthweight, what are the two limits for
normality?
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x1
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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
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Distribution of CHD according to body weight
status
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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 Hypothyroid Group Hypothyroid Group Hypothyroid Group Hypothyroid Group
1,1 1,7 2,1 2,7 3,4
1,1 1,7 2,1 2,7 3,4
1,1 1,7 2,1 2,8 3,4
1,1 1,7 2,4 2,9 3,4
1,1 1,9 2,4 2,9 3,4
1,2 1,9 2,4 2,9 3,4
1,2 2,0 2,4 2,9 3,4
1,4 2,0 2,4 2,9 3,5
1,5 2,0 2,5 3,0 3,5
1,5 2,0 2,5 3,1 3,7
1,5 2,0 2,5 3,1 3,7
1,5 2,0 2,6 3,1 3,9
1,5 2,0 2,6 3,4 3,9
1,6 2,1 2,7 3,4 3,9
1,6 2,1 2,7 3,4 4,0
Euthyroid Group Euthyroid Group Euthyroid Group Euthyroid Group Euthyroid Group
1,6 4,5 5,5 6,9 8,4
2,1 4,8 5,6 7,1 8,6
2,4 4,8 5,7 7,1 8,6
2,4 4,8 5,7 7,1 8,7
2,8 4,8 6,0 7,1 9,6
3,0 4,8 6,1 7,2 9,6
3,0 4,9 6,1 7,5 9,6
3,4 5,0 6,1 7,6 9,6
3,4 5,0 6,4 8,0 9,7
3,8 5,0 6,4 8,0 9,9
4,0 5,1 6,4 8,1 9,9
4,0 5,1 6,6 8,1 10,4
4,2 5,1 6,7 8,1 10,9
4,2 5,5 6,7 8,4 11,4
4,3 5,5 6,9 8,4 12,5
Hyperthyroid Group Hyperthyroid Group Hyperthyroid Group Hyperthyroid Group Hyperthyroid Group
9,4 11,2 12,4 13,9 15,0
9,4 11,2 12,6 13,9 15,0
9,5 11,2 12,7 14,0 15,0
9,6 11,3 12,7 14,2 15,1
10,0 11,8 12,7 14,2 15,6
10,0 11,8 13,0 14,2 15,6
10,0 11,8 13,2 14,2 16,2
10,3 12,0 13,2 14,2 16,3
10,3 12,1 13,4 14,4 16,4
10,3 12,1 13,5 14,6 16,7
10,9 12,1 13,5 14,7 16,7
11,0 12,1 13,5 14,7 16,7
11,0 12,1 13,5 14,7 16,7
11,0 12,4 13,6 14,8 17,9
11,2 12,4 13,6 14,8 18,1
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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