Question

Construct and explain a histogram by choosing an external law enforcement related data series. Examples of external data are reports published by the FBI or NIJ. include the following three elements:

1. frequency distribution table for the data selected (includes cumulative frequency, relative frequency, and cumulative relative frequency)
2. histogram graph based on the frequency distribution
3. summary paragraph discussing observations and conclusions

Answer 1

Consider the following dataset showing the net increase in the external law enforcement personnel, for every 4-year period, from 1992-2012:

Years	Net increase(in thousands)
1992-1996	47
1996-2000	51
2000-2004	58
2004-2008	36
2008-2012	33

Note: This dataset is not an original dataset and is made up only for illustrative purposes. However, related original datasets can easliy be found.

Now, the frequency distribution for the given data is given below:

Frequency distribution

Years	Frequency (in thousands)	Relative Frequency	Cumulative Frequency	Cumulative Relative Frequecy
1992-1996	47	47/225 = 0.2089	47	0.2089
1996-2000	51	51/225 = 0.2267	47+51 = 98	0.2089+0.2267 = 0.4356
2000-2004	58	58/225 = 0.2578	98+58 = 156	0.4356+0.2578 = 0.6934
2004-2008	36	36/225 = 0.16	156+36 = 192	0.6934+0.16 = 0.8534
2008-2012	33	33/225 = 0.1466	192+33 = 225	0.8534+0.1466 = 1
Total	225	1

The calculations for relative frequencies, cumulative frequencies and cumulative relative frequencies are shown in the table itself.

The required histogram is:

Observations & Conclusions:

A histogram is defined as the graphical representation of any numerical data in order to provide a better visual understanding of the distribution of data. On the other hand, a frequency distribution is the tabular representation of data.

The frequency distribution given above shows that there has been a total increase of 225,000 in the law enforcement personnel between 1992 - 2012. From the histogram, it can be clearly seen that maximum increase in the enforcement personnel happened during the period 200-2004, which is 58,000.It also shows that there has been a continuos increase from 1992 - 2004 but it showed a decline from 2004 - 2012. There is a significant decline in the period 2004 - 2008.