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 ( xm) N° of local units (f) fxm  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 Σfxm= 377925 Σfx2= 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

Formula

where x= the midpoint of a class interval.

Formula

Median

Formula

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

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

Formula

Standard Deviation

Formula

Table 5

Employment size Midpoint ( xm) N° of local units (f)  fxm   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 Σfxm= 285627.5 Σfx2= 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

Mean, Median, and Standard deviation for Hotel & Catering in the UK for the 2007

Mean

Formula

where x= the midpoint of a class interval.

Formula

Median

Formula

Since n/2 = 10907.5, therefore, median class is 5 to 9.

F = 9980, fm = 4940, h = 5, Lm = 9.5

Formula

Standard Deviation

Formula

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