## References

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### BUS1100 Assignment 1

Statistical Analysis and Report Writing

Name: John Smith

Student number: 31075698

Tutor's name: David Jones

Tutorial time: 2pm Wednesday

 List of Tables i List of Figures i 1 Introduction 1 2 Data Analysis 2 3 Conclusion 3 References 7 Appendices 8

### List of tables

 Table 1: Initial Summary Statistics of the Sample 2 Table 2: Measures of Central Tendency 3 Table 3: Measures of Dispersion for Manufacturing Sectors 5 Table 4: General Statistics of Manufacturing Sectors 5

### List of figures

 Figure 1: Histograms of Data from Different Manufacturing Sectors 3 Figure 2: Boxplot Comparison of Net Assets 4

### 1 Introduction

This report uses a descriptive statistical method to analyse and compare the net assets (\$m) of a sample of companies in four different manufacturing sectors; Sector A, Sector B, Sector C and Sector D. For the purposes of the report it is assumed that the sample of data analysed for each sector is representative of the entire population of companies. However a comparison of the data is limited by the varied number of observations for each sector. The discussion presents an analysis of the data using descriptive measures of frequency distribution, central tendency and standard deviation which reveal similar net asset figures between the four different manufacturing sectors.

### 2 Data analysis

To enable a comparison of the net assets (individual data, in million dollars, \$m) of the companies in the four different manufacturing sectors a random sample from each of these populations was made (see Appendix I)

. .............................................. [topic sentence only]

Sector 1

(\$,m)
Sector 2

(\$,m)
Sector 3

(\$,m)
Sector 4

(\$,m)
Count (no. of companies) 73 45 19 50
Sum 24177.9 13284.6 5347.9 13941.9
Range 1570.5 1063.4 444.3 1746.0

Table 1: Initial Summary Statistics of the Sample.

(Summary statistics have been rounded off to one decimal place to maintain clarity.)

It can be seen from Table 1 that far less samples were obtained from Sector 3 than the other sectors. This could have resulted in a significantly lower range because there was less pportunity for an individual company to have extremely high or low assets. As the number of companies in each sector increased, so did the sum of their total net assets. This is significant because it indicates that the majority of companies throughout manufacturing sectors had similar net asset values.

The general spread of net assets for each sector can be seen by allocating the raw net asset figures into frequency distributions and then histograms for each of the four manufacturing sectors. Using histograms as a graphical representation 'allows us to comprehend the shape of frequency distribution at a glance' (Harrison and Tamaschke, 1993, p. 91) and is therefore a quick and easy way to determine the asset distribution for each sector. 5.1

Figure 1: Histograms of Data from Different Manufacturing Sectors

(Note the histograms were obtained using Minitab for Windows, with 24 intervals between the range of 0-600 \$m, thus midpoints were allocated every 25\$m. A number of few extreme values have been omitted to provide a more precise representation of the majority of the data within each manufacturing sector. For full histograms covering the entire range of values refer to Appendix 2.)

The histograms of the manufacturing Sectors 1-4 are illustrated in Figure 1

. . . ................................................ [topic sentence only]

Sector 1

(\$,m)
Sector 2

(\$,m)
Sector 3

(\$,m)
Sector 4

(\$,m)
Median 306.2 308.2 290.5 317.2
Mean 331.2 295.2 281.5 278.8
Trimmed mean 316.9 201.1 295.7 300.9

Table 2: Measures of Central Tendency.

As indicated in Table 2, we can see that the median and both means for all manufacturing sectors are close to the suspected 300 \$m figure. 'Measure of central tendency is defined as a single term that is considered most representative of the whole set of data' (Johnson, 1978, p. 182) thus using a mode for this value would be inappropriate (see Appendix 1) 5.2 The reason for this is that three of the manufacturing sectors contained more than one net asset figure as the most common. In Sector 4, the minimum value was also a modal value, certainly not representing where the majority of data lies. The problem in using the mode arises from the fact that continuous data with two decimals is used for the initial net asset values, thus it is rare that two companies have equal net assets in any given sector.

Figure 2: Boxplot comparison of Net Assets (\$,m)

A large difference between the median and mean for Sectors 1 and 4 respectively is apparent upon looking at Table 2 . In sector 1, the mean is far higher than the median. This is due to one company having an extremely large net asset figure (\$1530.06 \$m), and many outliers above the mean (see Figure 2). . .

..........................................[this paragraph continues]

Sector 1

(\$,m)
Sector 2

(\$,m)
Sector 3

(\$,m)
Sector 4

(\$,m)
Standard Deviation 169.5 168.0 95.5 249.3
Sample Variance 28742.6 28239.6 9123.1 62166.3
Inter-Quartile Range 55 109.2 67.6 122.6

Table 3: Measures of Dispersion for Manufacturing Sectors

From Table 3 it can be seen that the standard deviation for Sectors 1 and 4 are distorted by the exceptionally large and small values within each of these sectors.

. . . ............................................... [topic sentence only]

Sector 1

(\$,m)
Sector 2

(\$,m)
Sector 3

(\$,m)
Sector 4

(\$,m)
Minimum -40.5 -261.2 -69.8 -512.9
10th percentile 267.2 188.6 237.6 157.3
Lower Quartile 289.3 245.4 260.4 231.4
Median 306.2 308.2 290.5 317.2
Upper Quartile 344.3 354.6 232.0 354.0
90th Percentile 423.5 433.3 365.9 422.2
Maximum 1530.1 802.3 374.5 1233.2

Table 4: General Statistics of Manufacturing Sectors (calculated in Minitab)

An examination of Table 4 provides some further interesting observations. . .

.. ............................................. [topic sentence only]

### 3 Conclusion

The data from four different manufacturing sectors has been analysed through the use of descriptive measures of central tendency, frequency distribution, and standard deviation. Robust statistics were also deployed to provide a better indication of net asset values within sectors with extreme values as these values can distort calculations of central tendency and dispersion. The relatively close measures of central tendency identified in the analysis suggest that although the spread of assets between the sectors differs; sectors 1 and 3 had small spreads of assets and sectors 2 and 4 had a larger net asset range, the majority of companies across the four sectors have similar net asset values; a higher frequency of assets values at approximately 300 (\$m).

### References 5.3

Harrison, S. and Tamaschke, R.H.U. (1993) Statistics for business economics and management. Sydney: Prentice Hall.

Johnson, P.R. (1978) Business statistics. Sydney: MacMillan.

Luxford, K., Bedingfield, S. and Betts, J. (1998) Course notes for BUS1100 Qualitative methods for business systems. Melbourne: Monash University.

Mansfield, E. (1994 ) Statistics for business and economics and methods and applications. New York: Norton.

### Appendices

Appendix 1 Random Sample of Data

Appendix 2 Histograms of the entire range of company net assets (\$m) values for the four manufacturing sectors

Appendix 3 The frequency distribution of assets from the four manufacturing sectors

#### Quoting

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Using histograms as a graphical representation provides an overview of the shape of frequency distribution (Harrison and Tamaschke, 1998). . .

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#### Referencing

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