Data Distribution Analysis

This assignment focuses on analyzing the distribution of two variables: HOME (representing housing type) and ARREST (representing arrest records). Students are tasked with determining the mode for each variable and evaluating whether the data follows a normal distribution. The analysis includes examining summary statistics like mean, standard deviation, skewness, and kurtosis to draw conclusions about the shape and characteristics of the distributions. Understanding the distribution of these variables is crucial for interpreting statistical results and making informed decisions in various fields.

1. For the variable HOME, what are the modes? Is the data normally distributed?
Value Label Value Frequency Percent Valid Percent Cumulative
Percent
House 1 280 81.6 82.4 82.4
Duplex 2 3 .9 .9 83.2
Trailer 3 34 9.9 10.0 93.2
Apartment 4 21 6.1 6.2 99.4
Other 5 2 .6 .6 100.0
Missing 3 .9
Total 343 100.0 100.0
HOME
N Valid 340
Missing 3
Mean 1.41
Std. Error of Mean .051
Median 1
Mode 1
Std. Deviation .945
Variance .892
Skewness 2.001
Std. Error of Skewness .132
Kurtosis 2.613
Std. Error of Kurtosis .264
Range 5
Answer:
The mode of a variable data is the value that occurs for a maximum number of times in
the variable data. In other words, it is a value that occurs more often than any other value.
As observed from the summary statistics table above, the mode value is 1, suggesting that
the value label ‘House’ is the most frequently occurring value in the sampled data for the
variable HOME. The frequency of ‘House’ is 280 or approx. 81.6% of the total sampled
values.
Further, as evident from the skewness and kurtosis factors, the sample data does not have
an approximately normal distribution. The shape of the distribution, as such, is
asymmetric and is skewed to the right (i.e. has positive skewness).
2. For the variable ARREST, what are the modes? Is the data normally distributed?

ARREST
Value Label Value Frequency Percent Valid Percent Cumulative
Percent
0 243 70.8 86.2 86.2
1 23 6.7 8.2 94.3
2 10 2.9 3.5 97.9
3 3 .9 1.1 98.9
5 2 .6 .7 99.6
24 1 .3 .4 100.0
Missing 61 17.8
Total 343 100.0 100.0
N Valid 282
Missing 61
Mean .30
Std. Error of Mean .093
Median 0
Mode 0
Std. Deviation 1.567
Variance 2.455
Skewness 12.692
Std. Error of Skewness .145
Kurtosis 187.898
Std. Error of Kurtosis .289
Range 24
Answer:
As observed from the summary statistics table above, the mode value is 0, suggesting that
the most frequently occurring value in the sampled data for the variable ARREST is ‘0’.
In other words, a maximum proportion of the sampled persons have a record of ‘zero’
arrests. The frequency of ‘0’ arrests is 243 or approx. 70.8% of the total sampled values.
Again, as evident from the ‘significantly high’ values of skewness and kurtosis factors, it
the sample data does not have an approximately normal distribution. The shape of the
distribution, as such, is asymmetric and is ‘heavily’ skewed to the right (i.e. has positive
skewness).

3. What difference does it make in the case of each of the variables (HOME and ARREST) if the
data is not normally distributed?
Answer:
In case, each of the variables (HOME and ARREST) is not normally distributed, the variable
data cannot be used to perform any statistical tests, or as such, draw any reliable conclusions
using the descriptive summary for the sample data or for the general population (in concern).
Moreover, the techniques of statistical inference cannot be used in such cases as it is very likely
that the sample data is not a true representation of the broader population and thus, can lead to
wrong interpretations of results.