Research Method
Question 2 Part (a)
Table 1; Data Summary
∑f=80
Calculations
The sample arithmetic mean
x ̅=( ∑▒〖(MI)×f〗)/(∑▒f) =1535/80=19.19
The median x ̅ =〖 L〗_(1 )+( (N/2-∑▒〖fmed )×c〗)/fmed =15+((40-27))/((22))×5 = 15 + 2.95 = 17.95
〖 L〗_(1 )=Lower class limit of the median
N=Total Frequency
∑▒█(fmed )=Sum of the frequencies of classes below the median class@) fmed =Frequency of the median class c=Width of the median class
The mode
(X ) ̂=〖 L〗_(1 )+ (f_(0-f_1 )/(2 f_0-f_(1 - ) f_2 ))×h =15+(22-19)/(2(22)-19-13) ×5 =15+3/10×5 =16.25
Where
L_(1 )= Lower boundary of class containing mode f_(0= )Frequency of modal class f_(1 )= Frequency of class preceding modal class f_( 2)= Frequency of class after modal class h= Class width The inter-quartile range
X_(25=) 10+((20-8) )/((27-8) ) × 5 =10+12/19 ×5 =13.16
X_(50=) 15+((40-27) )/((49-27) )×5 =15+(13 )/(22 )×5 =17.95
X_(75=) 20+((60-49) )/((62-49) )×5 =20+((11) )/((13) )×5 =24.23
Interquartile range = X_(75 ) - X_25= 24.23-13.16=11.07
Lower quartile is define as X_(25 )and upper quartileX_75. The standard deviation
S= √( (〖(MI)〗^2×f)/(n-1)-x^(-2)=√(34400/79)) -〖19〗^2
=√(435.443-361)
=√74.443
=8.62
Question 2 Part (b)
REPORT ON THE SUMMURISED DATA
1.0 Introduction
The Board of management of a not-for-profit organisation has commissioned a study to determine the length of time (in months) that clients using it counselling services have been unemployed.
2.0 Methodology
A random sample consisting of 80 service recipients were selected for the study and each of the recipients was asked how many months they have been unemployed. The response received were tabulated and analysed using measures of central tendency, standard deviation, and interquartile range. The resulting characteristics of the data are summarised in this report.
3.0 Summary of data
.
Table 1; Data Summary
∑f=80
Calculations
The sample arithmetic mean
x ̅=( ∑▒〖(MI)×f〗)/(∑▒f) =1535/80=19.19
The median x ̅ =〖 L〗_(1 )+( (N/2-∑▒〖fmed )×c〗)/fmed =15+((40-27))/((22))×5 = 15 + 2.95 = 17.95
〖 L〗_(1 )=Lower class limit of the median
N=Total Frequency
∑▒█(fmed )=Sum of the frequencies of classes below the median class@) fmed =Frequency of the median class c=Width of the median class
The mode
(X ) ̂=〖 L〗_(1 )+ (f_(0-f_1 )/(2 f_0-f_(1 - ) f_2 ))×h =15+(22-19)/(2(22)-19-13) ×5 =15+3/10×5 =16.25
Where
L_(1 )= Lower boundary of class containing mode f_(0= )Frequency of modal class f_(1 )= Frequency of class preceding modal class f_( 2)= Frequency of class after modal class h= Class width The inter-quartile range
X_(25=) 10+((20-8) )/((27-8) ) × 5 =10+12/19 ×5 =13.16
X_(50=) 15+((40-27) )/((49-27) )×5 =15+(13 )/(22 )×5 =17.95
X_(75=) 20+((60-49) )/((62-49) )×5 =20+((11) )/((13) )×5 =24.23
Interquartile range = X_(75 ) - X_25= 24.23-13.16=11.07
Lower quartile is define as X_(25 )and upper quartileX_75. The standard deviation
S= √( (〖(MI)〗^2×f)/(n-1)-x^(-2)=√(34400/79)) -〖19〗^2
=√(435.443-361)
=√74.443
=8.62
Question 2 Part (b)
REPORT ON THE SUMMURISED DATA
1.0 Introduction
The Board of management of a not-for-profit organisation has commissioned a study to determine the length of time (in months) that clients using it counselling services have been unemployed.
2.0 Methodology
A random sample consisting of 80 service recipients were selected for the study and each of the recipients was asked how many months they have been unemployed. The response received were tabulated and analysed using measures of central tendency, standard deviation, and interquartile range. The resulting characteristics of the data are summarised in this report.
3.0 Summary of data
.
References: I.P.A (Institute of Public Administration), 2010, Research Method Handbook. Verlinden.J. A. 2010 beginner guide to communication research method. H.Learn, 2008. Analyse this, Learn how to analyse data [online] available at http://learnhigher.ac.uk/analysethis/index.html [accessed 22 November 2011] H.J. Streubert and D.R. Carpenter (1999). Qualitative Research in Nursing: Advancing the Humanistic Imperative. 2nd ed. Philadelphia