The Distribution of Employment Size

The distribution of employment size (number of employees) for different categories of businesses varies depending upon the need of the business. In this report, the distribution of employment size for Retail and Hotel & Catering business division in London for the year 2007 will be compared.

Table 1 shows the distribution of employment size for the Retail sector in London for the year 2007. About 65% of local units have employment sizes 0 to 4, and about 19% of local units have employment sizes 5 to 9. Further, about 93% of local units have an employment size of less than 20. Only, about 7% of local units have an employment size equal to or greater than 20.

Table 2 shows the distribution of employment size for Hotel & Catering in London for the year 2007. About 46% of local units have employment sizes 0 to 4; about 23% of local units have employment sizes 5 to 9, and about 19% of local units have employment sizes 10 to 19. Further, about 87% of local units have an employment size of less than 20. Only, about 13% local units have employment size equal to or greater than 20.

The average employment size for Retail sector is about 10. More than half of the units in the Retail sector have an employment size greater than 3. The standard deviation of the employment size for the Retail sector is about 39. The coefficient of variation for the Retail sector is about 380%. The mean is greater than the median value that suggests that the distribution of the employment size for the Retail sector is skewed to right (positively skewed).

The average employment size for Hotel & Catering is about 13. More than half of the units in Hotel & Catering have an employment size greater than 5. The standard deviation of the employment size for Hotel & Catering is about 38. The coefficient of variation for the Hotel & Catering is about 266%. The mean is greater than the median value that suggesting that the distribution of the employment size for Hotel & Catering is skewed to right (positively skewed).

In conclusion, the Hotel & Catering business divisions in London employ more people on average as compared to the Retail sector in London. Further, the spread of the Hotel & Catering business divisions in London is less as compared to the Retail sector in London. The majority of the local units of the Retail sector have an employment size less than or equal to four. However, for the Hotel & Catering business divisions, the majority of the local units have an employment size equal to or greater than five.

Table 1: The distribution of employment size for Retail sector in London, 2007

Employment size	N° of local units	Relative Frequency	Cumulative Relative Frequency
0 to 4	24085	0.6510	0.6510
5 to 9	7005	0.1893	0.8404
10 to 19	3260	0.0881	0.9285
20 to 49	1650	0.0446	0.9731
50 to 99	500	0.0135	0.9866
100 to 249	315	0.0085	0.9951
250 to 499	135	0.0036	0.9988
500 +	45	0.0012	1.0000
Total	36995	1.0000

Table 2: The distribution of employment size for Hotel & Catering in London, 2007

Employment size	N° of local units	Relative Frequency	Cumulative Relative Frequency
0 to 4	9980	0.4575	0.4575
5 to 9	4940	0.2264	0.6839
10 to 19	4145	0.1900	0.8739
20 to 49	2035	0.0933	0.9672
50 to 99	455	0.0209	0.9881
100 to 249	190	0.0087	0.9968
250 to 499	50	0.0023	0.9991
500 +	20	0.0009	1.0000
Total	21815	1.0000

Table 3

Employment size	Midpoint ( x_m)	N° of local units (f)	fx_m	*fx²*
0 to 4	2	24085	48170	96340
5 to 9	7	7005	49035	343245
10 to 19	14.5	3260	47270	685415
20 to 49	34.5	1650	56925	1963913
50 to 99	74.5	500	37250	2775125
100 to 249	174.5	315	54967.5	9591829
250 to 499	374.5	135	50557.5	18933784
500 +	750	45	33750	25312500
Total		N = 36995	£fx_m= 377925	£*fx²*= 59702150

Table 4

Employment size	N° of local units	Cumulative Frequency
0 to 4	24085	24085
5 to 9	7005	31090
10 to 19	3260	34350
20 to 49	1650	36000
50 to 99	500	36500
100 to 249	315	36815
250 to 499	135	36950
500 +	45	36995
Total	36995

Mean, Median, and Standard deviation for Retail sector in the UK for 2007

Mean

where x_m= the midpoint of a class interval.

Median

Since n/2 = 18497.5, therefore, median class is 0 to 5.

F = 0, fm = 24085, h = 5, Lm = -0.5

Standard Deviation

Table 5

Employment size	Midpoint ( x_m)	N° of local units (f)	fx_m	*fx²*
0 to 4	2	9980	19960	39920
5 to 9	7	4940	34580	242060
10 to 19	14.5	4145	60102.5	871486.3
20 to 49	34.5	2035	70207.5	2422159
50 to 99	74.5	455	33897.5	2525364
100 to 249	174.5	190	33155	5785548
250 to 499	374.5	50	18725	7012513
500 +	750	20	15000	11250000
Total		N = 21815	£fx_m= 285627.5	£*fx²*= 30149049

Table 6

Employment size	N° of local units	Cumulative Frequency
0 to 4	9980	9980
5 to 9	4940	14920
10 to 19	4145	19065
20 to 49	2035	21100
50 to 99	455	21555
100 to 249	190	21745
250 to 499	50	21795
500 +	20	21815
Total	21815