27-05-201
ObjECtIVEs
bIOstAtIstICs • Measures of central tendency
• Measures of variation
• Tests of significance
Dr. Pranay Jadav Chi square test
Assistant professor
Department of Community Medicine T-test
GMERS, Gandhinagar
Z-test
27-05-2016 1 27-05-2016 2
MEAN ( ) MEDIAN (M) MODE (Z)
mEAsuRE OF CENtRAl tENDENCy Ungrouped ∑ Most frequent observation in
= Odd case = th value in series
data the series.
Even case =
• Mean (Arithmetic mean/Average)
Grouped ∑ .
• Median data
=
∑ M= + ×C Z= + ×C
2fm f1 f2
Where
Where Where,
• l =lower limit of modal
f = frequency • l = lower limit of median class
• Mode • n= total number
class
x = variable • Fm =freq. of modal class
Σf = n • C.f< = cumulative freq.
• F1 =freq. just before mode
preceding median class
class.
• F = frequency of median class
• F2 =freq. after mode class.
• C= class interval
27-05-2016 3 27-05-2016
• C = class interval 4
EXERCIsE
RElAtION bEtwEEN mEAN, mEDIAN & mODE
You have collected the following data:
Mode = 3(Median)- 2(Mean)
17, 16, 21, 18, 13, 16, 12, 11.
Z=3M–2
Describe the data in terms of central tendency.
27-05-2016 5
Biostatistics
, 27-05-201
mEAN mEDIAN
Raw Data: 17 16 21 18 13 16 12 11
∑ Ordered: 11 12 13 16 16 17 18 21
=
Position: 1 2 3 4 5 6 7 8
N = 8, Even number
17 + 16 + 21 + 18 + 13 + 16 + 12 + 11
=
8
Median in Even case =
= 15.5 M= = 16
27-05-2016 7 27-05-2016 8
mODE EXERCIsE
17, 16, 21, 18, 13, 16, 12, 11
Find Median and Mode for following data
Mode (Z) =Most frequent observation
Age group 20-30 30-40 40-50 50-60 60-70
(years)
No. of persons 3 20 27 15 9
Z=16
27-05-2016 9 27-05-2016 10
CAlCulAtION OF mEAN FOR mEDIAN
Mid. Value
Age group No. of persons
Class interval Frequency (f) Cumulative Frequency. ( C.F )
20-30 03 25 75 20 - 30 3 3
30-40 20 35 700 30 - 40 20 23
40-50 27 45 1215 40 - 50 27 50
50-60 15 55 825 50 - 60 15 65
60-70 09 65 585
60 - 70 9 74
n=∑ =74 ∑ =3400
N=74
∑ 3400
n/2=37
= = = 45.94 years
∑ 74
27-05-2016 11 27-05-2016 12
Biostatistics
ObjECtIVEs
bIOstAtIstICs • Measures of central tendency
• Measures of variation
• Tests of significance
Dr. Pranay Jadav Chi square test
Assistant professor
Department of Community Medicine T-test
GMERS, Gandhinagar
Z-test
27-05-2016 1 27-05-2016 2
MEAN ( ) MEDIAN (M) MODE (Z)
mEAsuRE OF CENtRAl tENDENCy Ungrouped ∑ Most frequent observation in
= Odd case = th value in series
data the series.
Even case =
• Mean (Arithmetic mean/Average)
Grouped ∑ .
• Median data
=
∑ M= + ×C Z= + ×C
2fm f1 f2
Where
Where Where,
• l =lower limit of modal
f = frequency • l = lower limit of median class
• Mode • n= total number
class
x = variable • Fm =freq. of modal class
Σf = n • C.f< = cumulative freq.
• F1 =freq. just before mode
preceding median class
class.
• F = frequency of median class
• F2 =freq. after mode class.
• C= class interval
27-05-2016 3 27-05-2016
• C = class interval 4
EXERCIsE
RElAtION bEtwEEN mEAN, mEDIAN & mODE
You have collected the following data:
Mode = 3(Median)- 2(Mean)
17, 16, 21, 18, 13, 16, 12, 11.
Z=3M–2
Describe the data in terms of central tendency.
27-05-2016 5
Biostatistics
, 27-05-201
mEAN mEDIAN
Raw Data: 17 16 21 18 13 16 12 11
∑ Ordered: 11 12 13 16 16 17 18 21
=
Position: 1 2 3 4 5 6 7 8
N = 8, Even number
17 + 16 + 21 + 18 + 13 + 16 + 12 + 11
=
8
Median in Even case =
= 15.5 M= = 16
27-05-2016 7 27-05-2016 8
mODE EXERCIsE
17, 16, 21, 18, 13, 16, 12, 11
Find Median and Mode for following data
Mode (Z) =Most frequent observation
Age group 20-30 30-40 40-50 50-60 60-70
(years)
No. of persons 3 20 27 15 9
Z=16
27-05-2016 9 27-05-2016 10
CAlCulAtION OF mEAN FOR mEDIAN
Mid. Value
Age group No. of persons
Class interval Frequency (f) Cumulative Frequency. ( C.F )
20-30 03 25 75 20 - 30 3 3
30-40 20 35 700 30 - 40 20 23
40-50 27 45 1215 40 - 50 27 50
50-60 15 55 825 50 - 60 15 65
60-70 09 65 585
60 - 70 9 74
n=∑ =74 ∑ =3400
N=74
∑ 3400
n/2=37
= = = 45.94 years
∑ 74
27-05-2016 11 27-05-2016 12
Biostatistics
