Question

Project Questions:
Apply the statistical techniques and completely describe your data set for both variables in the light of following questions: Each (X,Y) has 20 observations.
a.   Discuss the types and level of measurement of the variables in the data.
b.   Prove that A.M>G. M>H.M (For both the variables).
c.   Estimate the values of Q3, D7 and P49 and Interpret the results.
d.   Compare Relative Dispersions of X and Y. Using (i) Quartile Coefficient of Dispersion and (ii) Coefficient of Variation.
e.   Explain whether the above two measures in part (d) provide the same information.
f.   Which Variable is more consistent.
g.   Discuss the shape of the variables X and Y using results of Mean, Median and Mode.
h.   Obtain skewness by Karl Pearson’s formula, For which variable (X,Y) skewness is more sharp.
i.   Obtain the Bowley’s coefficient of skewness. Is there any change in the decision regarding the shape of the variables?
j.   Draw a scatter plot of the data.
k.   Obtain Pearson’s coefficient of Correlation and interpret the results.
l.   Discuss what changes will there be on the value of the correlation coefficient if we transform variables X (first variable in the data) and Y (second variable in the data) using the following expressions. will there be any change in the value of rxy, if so then why or if not then why, please discuss.
u= 5x+46 and v=3y+2

X: Crime Rate (number of offences per million population)
Y: Expenditure (per capita expenditure on police)
X   45.5   52.3   56.6   60.3   64.2   67.6   70.5   73.2   75   78.1   79.8   82.3   83.1   84.9   85.6   88   92.3   94.3   95.3   96.8
Y   69   55   47   46   106   67   63   66   56   51   45   97   62   118   58   71   74   128   90   58

Answer 1

a).

X: Crime Rate (number of offences per million population)
Y: Expenditure (per capita expenditure on police)
X   45.5   52.3   56.6   60.3   64.2   67.6   70.5   73.2   75   78.1   79.8   82.3   83.1   84.9   85.6   88   92.3   94.3   95.3   96.8
Y   69   55   47   46   106   67   63   66   56   51   45   97   62   118   58   71   74   128   90   58

b).

	X	Y
Arithmetic Mean =	76.29	71.35
Geometric Mean =	74.77	68.02
harmonic Mean =	73.12	65.21

Clearly, AM > GM > HM for the variables

c).

	X	Y
Q3	86.20	78.00
D7	85.11	71.90
P49	78.59	63.87

d).

For quartile deviation we use IQR = Q3-Q1

	X	Y
Q3	86.20	78.00
Q1	66.75	55.75
IQR	19.45	22.25
1.5*IQR	29.18	33.38
Coefficient of variation=	0.19	0.33

e).

The above two computations are both measures of dispersion and variation.

f). The one with less CV is more stable. X is more consistent

g).

	X	Y
Mean	76.29	71.35
Median	78.95	64.50
Mode	#N/A	58.00

Here, Mean > Median > Mode

Therefore, the distributions are Right skewed.

Please rate my answer and comment for doubt.