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Application: Measures of Central Tendency, The Battawba
Essay Instructions:
Application: Measures of Central Tendency
Measures of central tendency may be familiar to you from prior math classes you have taken. Consider the summary of these terms below:
- The mean is the average of all numbers in a set of data.
- The mode is the number in a dataset that most frequently occurs.
- The median is the number that falls in the middle of the numbers in a given set when those numbers are placed in rank order.
- The standard deviation tells how far the numbers in a given data set deviate from the mean of that set. In other words, it tells whether the numbers in the dataset are generally close together or far apart.
These measures are simple but extremely valuable for all social scientists, including criminal justice researchers. They are summary statistics, which provide useful information about the study sample and allow researchers to compare multiple data sets.
For this Application Assignment, use the following statistics:
The total population of the Battawba metropolitan area was 5,604,383 persons in 2011. For that year, the following burglary rates were reported in the localities within this metropolitan area:
Essay Sample Content Preview:
Application: Measures of Central Tendency
Name
Institution
Date
The total population of the Battawba metropolitan area was 5,604,383 persons in 2011. For that year, the following burglary rates were reported in the localities within this metropolitan area:
AreaNumber of Burglaries ReportedCity of Battawba2,563City of Wineburg734City of Lakeville301City of Drake1,482City of Valmer231City of Chase Abbey857City of Southmetro644City of Collington1026City of Williamson644City of New Batten
159
1] Calculate the mean, median, mode, and standard deviation for the burglary statistics provided on the metropolitan area of Battawba.
Mean=Sum of values/ number of values= ∑/n
= (2,563+734+301+1,482+231+857+644+1026+644+159)/ 10= 8641/10=864.1
Median= rearranging the data then this is 159,231,301,644,644,734,857,1026,1482,2563
As such, Median = (644+734)/ 2= 1,378/2= 689
Mode, is the most frequent value= 644
Standard Deviation=716.72
AreaNumber of Burglaries ReportedX-M(X-M)^2City of Battawba2,5631,6992886261City of Wineburg734-13016926.01City of Lakeville301-563317081.6City of Drake1,482618381800.4City of Valmer231-633400815.6City of Chase Abbey857-750.41City of Southmetro644-22048444.01City of Collington
1026
162
26211.61
City of Williamson
644
-220
48444.01
City of New Batten
159
-705
497166
Total
864.1
4,623,201
Standard deviation (s) = √X-M/ n-1= √4,623,201/ (10-1) = √ 513689=716.72
Explain your interpretation of the measures of central tendency and standard deviation for burglary rates in the Battawba metropolitan area (i.e., what they can tell you about who is committing crime and where it is being committed).
As the mean burglary rates is 864.1, there are three cities with higher than average burglary crime rates, the City of Battawba (2563 cases), City of Drake (1,482 cases), and City of Collington (1,026 cases), while the other seven cities have lower burglary rates. The typical number of reported burglaries is 864 cases. When conducting hypothesis tests, it i...
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