Comparison of sales volumes
The mean is the average of values in a given set of data. In this case, the average sales volume gives the average volume of sales for each salesperson over the six week period. The means can be used to compare the sales volumes of the four salespersons and rank them. The mean is obtained by getting the sum of the volume of sales for all the six weeks then dividing by the number of weeks under consideration.
Determination of the mean volume of sales
Mean volume of sales = Total sales/6 weeks
Salesperson A = (1774 + 1808 + 1890 + 1932 + 1855 + 1726)/6
= 10985/6
= 1830.83
Salesperson B = (2205 + 1507 + 2352 + 1939 + 2052 + 1630)/6
= 11685/6
= 1947.5
Salesperson C = (1330 + 1295 + 1502 + 1104 + 1189 + 1441)/6
= 7861/6
= 1310.17
Salesperson D = (1402 + 1665 + 1530 + 1826 + 1703 + 1498)/6
= 9624/6
= 1604
Based on the above calculations, salesperson A had an average sales volume of 1,830.83 while salesperson B had an average volume of 1,947.5. Salesperson C had a mean sales volume of 1,310.17 while D had a mean sales volume of 1640. This implies that Salesperson B had the highest volume of sales based on the average volume of sales. He was followed by Salesperson A then Salesperson D. Salesperson C had the lowest sales volume of all the four salespersons.
Measure of consistency
Consistency can be measured by determining the dispersion of the sales volume figures from the average volume of sales. This can be given by the standard deviation or the coefficient of variation. The standard deviation measures the spread of values from the average value in a set of data (Mann, 2010). It is given by the square root of the mean squares of the deviations of all values from the average value. A greater standard deviation implies that there is a great dispersion in the data hence there is low consistency than when the standard deviation is lower. When comparing two or more variables, the variable that has the least standard deviation has the highest level of consistency while the variable with the greatest standard deviation is the least consistent.
When comparing given sets of data with different values, the coefficient of variation is a better measure of consistency or variation than the standard deviation (Mann, 2010). The coefficient of variation is the standard deviation per unit of the mean. It is a better measure than standard deviation since it takes into consideration the values of the variables. A variable may have a higher standard deviation because of the high values of data and not necessarily because of the low level of consistency. Since it is a relative measure, it is the most suitable measure for comparing consistency for variables with different means.
The standard deviation for Salesperson A is 69.59505889 while that of Salesperson B is 298.821435. Salesperson C has a standard deviation of 136.4592939 while that of Salesperson D is 141.6109694. Based on the standard deviation, Salesperson A was the most consistent of all the four salespersons since he had the least standard deviation. Salesperson C was the second most consistent salesperson while Salesperson D was the third most consistent. Salesperson B had the highest standard deviation hence he was the least consistent of the four salespersons.
Determination of coefficient of variation
Coefficient of variation = Standard deviation/Mean
Salesperson A =69.59505889 /1830.83 = 0.038012777
Salesperson B = 298.821435/1947.5 = 0.15344
Salesperson C = 136.4592939/1310.17 = 0.10415
Salesperson D = 141.6109694/1604 = 0.08829
Conclusion
The above analysis shows that Salesperson B has the highest volume of sales as shown by the average volumes of sales. However, Salesperson B is the least consistent of the four salespersons. Salesperson A had the second most sales but was the most consistent of the four salespersons. Salesperson A is the best due to the high volume of sales as well as the high level of consistency.
References
Mann, P. (2010). Introductory statistics (7th ed.). New York: John Wiley & Sons.
APPENDICES
Descriptive statistics (from excel)
