Descriptive Statistics Project: Police Municipality Data Analysis

This descriptive statistics project analyzes a dataset of black disparity indices across various police municipalities in St. Louis County. The project begins with a table presenting the 2014 black disparity index for different police departments. It includes frequency, relative frequency, and cumulative frequency tables, alongside a histogram illustrating the distribution of the data. The analysis calculates the mean, median, and mode, noting the data's skewness and the implications of these measures. Z-scores are computed for the highest, lowest, and mean values to understand data distribution relative to the mean. A 5-number summary is presented, along with a box and whisker plot to visualize the dataset's range and quartiles. The project concludes by discussing the limitations of the sample, the data's non-normal distribution, and the implications of the findings, emphasizing that the sample results cannot be logically extrapolated to the whole St Louis County and city area.

Descriptive Statistics Project
1) The 20 sample police Municipality and 2014 Black Disparity Index table
Police Municipality 2014 Black Disparity
Index
Brentwood Police Dept. 8.31
Breckenridge Hills Police Dept. 1.26
Ladue Police Dept. 15.98
Maryland Heights Police Dept. 2.86
Clayton Police Dept. 3.26
Des Peres Police Dept. 7.91
Bellefontaine Neighbors Police Dept. 1.07
Shrewsbury Police Dept. 4.76
Kirkwood Police Dept. 1.93
Pagedale Police Dept. 0.86
Chesterfield Police Dept. 4.49
Vinita Park Police Dept. 1.07
Hazelwood Police Dept. 1.89
Maplewood Police Dept. 2.33
University City Police Dept. 1.37
Manchester Police Dept. 2.21
Charlack Police Dept. 1.7
Sunset Hills Police Dept. 5.76
Beverly Hills Police Dept. 0.97
Bel-Nor Police Dept. 1.49
The above table shows the data set obtained from different police department municipalities across St.
Louis County and city. The above table represents various police departments’ municipalities along with
the 2014 black disparity indices. The 2014 black disparity index was calculated as follows;
Disparity index=proportion of black stops/proportion of blacks in the population
The data was specifically collected through stops, searches, arrests by the various police department
municipalities. The table also represents the population in each municipality. The table also shows the
20 sample department along with the 2014 black disparity, this random sample has been obtained using
the RANDBETWEEN functions in microsoft excel.
2)

2014 Black Disparity Index frequency table
2014 Black
Disparity
Index Frequenc
y
0.86 - 5.9 17
6.0 - 11.04 2
11.05 -16.09 1
Total 20
2014 Black Disparity Index relative frequency table
2014 Black
Disparity
Index Frequenc
y
Relative
Frequenc
y
0.86 - 5.9 17 0.85
6.0 - 11.04 2 0.1
11.05 -16.09 1 0.05
Total 20 1
2014 Black Disparity Index cumulative frequency
2014 Black
Disparity
Index Frequenc
y
cumulativ
e
frequenc
y
0.86 - 5.9 17 17
6.0 - 11.04 2 19
11.05 -16.09 1 20
Histogram of 2014 Black Disparity Index

Relative frequency histogram of
2014 black disparity indices
6 12 18 More
0
0.5
1
1.5
2
2.5
3
3.5
Frequency
2014 black disparity indices classes
Frequency
3) The mean of the 2014 Black Disparity Index is greater than both the median and mode.
These measures of center tendencies have impact on the given data set which is 2014
Black Disparity Index.
The 20 random samples do not represent a normal distribution this is because the mean,
mode and median are not equal to each other. Furthermore, the 20 random sample data
set of the 2014 Black Disparity Index is skewed to the right this is because the mean is
greater than the median.
4) The mean and standard deviation of the data set are 3.574 and 3.674 respectively (Ling,
2017). Therefore using the empirical rule which states that between 1 standard deviation
on either side of the mean (3.574+3.674) and (3.574-3.674) expect approximately 68% of
the scores to fall.
It further states that between 2 standard deviation on either side of the mean
(3.574+2(3.674)) and (3.574-2(3.674)) expect approximately 95% of the score fall.
6 12 18 More
0
0.5
1
1.5
2
2.5
Frequency
2014 black disparity indices classes
Frequency

Looking at the data set and comparing with this empirical rule, we find that it holds. This
is because about 68% of the data set falls within the first standard deviation from the
mean and also 95% falls within the two standard deviation of the data set.
5) Z-score of the highest element= (highest element-Mean)/standard deviation
= (x-μ)/σ
= (15.98-3.574)/3.674
=3.37666
Z-score of the smallest element= (smallest element-Mean)/standard deviation
= (x-μ)/σ
= (0.86-3.574)/3.674
=-0.73869
The Z-score of the smallest value is negative and therefore the 20 sample of 2014 Black
Disparity Index data set is below the mean. In addition the Z-score of the highest value is
positive and this implies that the score of the data set is above the mean.
The Z-score of the mean= (Mean-Mean)/standard deviation
= (μ-μ)/σ
= (3.574-3.574)/3.674
=0
The Z-score of the mean is zero because it’s equal to its mean.
6) The 5-number summary of the 20 random sample are calculated in excel and they
include;
Minimum value= 0.86
1st Quartile value = 1.3425
Median value= 2.07
3rd Quartile value= 4.557
Maximum value= 15.98
Box and Whiskers plot of the 20 random sample

Sample
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Box 3
Box 2
Box 1
The boxplot and whisker are used to indicate the overall trends of the data set. They also
provide a helpful visualization of the range and quartiles.
7) From the sample above we find that the measure of central tendencies are not equal that
is the mean is greater than both mode and median.
The findings from the dataset include that the z-score of the mean is zero and the box plot
and whisker are distributed from the mean.
The above data set is not normally distributed
The central tendency score shows that the dataset is skewed to the right. The data varies
from 0.86 to a maximum value of 15.98 and its range is 15.12 (Johnson and
Bhattacharyya, 2019).
The municipalities with a Black Disparity index of 0.86 and 15.98 did not quite seem to
follow along with the normal expectation.
The sample results cannot be logically extrapolated to the whole St Louis County and city
area. The Ferguson police department does not compare well with the rest of the county
using the findings from the sample. It was consider being a usual value compared to the
rest of the data.

References
Ling, T.J., 2017. Summarizing data using measures of central tendency: A group activity.
Johnson, R.A. and Bhattacharyya, G.K., 2019. Statistics: principles and methods. John
Wiley & Sons.