Business Decision Making
a)
x=1nx1+x2++xn
Where n is the number of cases.
Mean:
5.55+3.02+5.13+4.77+2.34+3.54+3.79+4.5+6.1+0.38+5.12+6.46+6.1913==4.38
Median value is the 50th percentile or the “middle” element of a sorted data set.
Sort the data in ascending order:
The middle element is 4.77
The expected waiting time for customers is 4.38 minutes. The 50-percentile (or the middle) time of waiting is 4.77 minutes.
b)
The so-called “five number summary” includes such statistical measures as sample minimum, sample maximum, first quartile, third quartile and range.
Sample minimum is 0.38
First quartile is 25th percentile; hence, it is equal to 3.54
Median is 4.77
Third quartile is the 75th percentile; hence, it is equal to 5.55
Sample maximum is 6.45
The waiting time varies from 0.38 minutes to 6.45 minutes. 25% of customers wait no more than 3.54 minutes, 50% - no more than 4.77 minutes, 75% - no more than 5.55 minutes.
c)
Sample variance can be calculated by using the following formula:
V=1n-1*i=1nxi-x2
Variance:
V=113-1*i=113xi-4.382≈3.01
Standard deviation is a square root of variance:
σ=V≈1.73
Coefficient of variation is equal to the ratio of standard deviation and mean value:
CV=σμ=1.734.38≈0.39
The average “distance” from the mean time of 4.38 minutes is 1.73 minutes. The coefficient of variation shows the measure of variation of the data in relation to mean value. It is equal to 39% in our case.
d)
Yes, the data is skewed, because median and mean are not equal. I would suggest to use median and IQR instead of mean and standard deviation. These measures are better for skewed data.
e)
I would like to say that the branch manager’s answer was quite deceiving. We calculated that only 75% of the customers are waiting less than 5.55 minutes. Hence, the percentage of those who wait less than 5 minutes is even lower. We cannot say that the probability less than 0.7 is “almost likely”. Brand manager was not accurate in his statement.
a)
Consider the scatter diagram (it was plotted in Excel):
It seems that there is a positive linear relationship between the variables, because as selling and distribution expenditures are increasing, sales in units are also being increased (and vice versa).
b)
Coefficient of correlation can be computed as follows:
r=ni=1nxi*yi-i=1nxi*i=1nyini=1nxi2-i=1nxi2*ni=1nyi2-i=1nyi2
However, it also possible to calculate it in Excel using function CORREL().
The coefficient of correlation is calculated in Excel:
r≈0.735
c)
The points on a scatter diagram are located closely to a straight line. The coefficient of correlation indicated strong positive linear relationship between the variables.
d)
The ratio of selling & distribution expenses to sales is calculated as value of expenditures divided by value of sales and multiplied by 100%.
Calculate the ratio:
The average percentage is 5.27%
The purpose of this task is to prepare a network diagram and determine the critical path. Network diagrams reflect a network model in graphical form as a set of vertices that correspond to work activities and lines that represent the relationship between the given activities. So, we put all the activities from A to J in rectangles (vertices) and connect them with lines that connect preceding and subsequent works. A network diagram was developed in https://www.draw.io/
The critical path of the network diagram is the complete path from the starting activity to the final activity that has the greatest length (duration) of all full paths. It determines the length of the time period of the implementation of all the works in the network. Obviously, the longest path is A-E-H-I-J and it is equal to 52 minutes.
