CASE STUDY:
Company X in Dubai have collected data about the revenues of their products at the end of 2020 in light of the impact of Pandemic COVID-19. Then, the top management required from you to do tasks supporting the organization statistically in making a set of decisions about urgent issues need to be done, and according to the following points:
If the average annual of the company’s revenues for 20 branches of the company is 850 thousand dirhams with a standard deviation (S) of 90 thousand dirhams, and the value of the most frequent (Mode) is 650 thousand dirhams, then it is required to determine:
To what extent is there a symmetry or skewness in the curve of sales data for these branches? Then determine the degree of skewness of this data curve if any and then determine the skew direction? Explain the expected relationship by drawing between each of three measures (the mean, mode, and median)?
Use the Chebyshev Inequality to determine the percentage of sales of these branches, which fall at least between 950 thousand dirham and 750 thousand dirham? Then determine the percentage of sales that fall outside this period?
If X denote the number of service visits of the maintenance centers which recorded through the same year to fix a certain problem regarding the products purchased from your company and the frequency of customers who visited these centers for this problem by the next table:
X 1 2 3 4 5
Freq. 20 15 20 35 10
Thus. calculate the following:
The relative frequency of each service visit.
The cumulative frequency.
The average of service visit.
The standard values of service visits to compare with the data of last year.
Regarding the customer of this company who were asked about a new product, if the probability that a randomly selected one was national people (E) is 0.898. And the probability that a randomly selected one is national people and is less than 20 years old 0.754, so try to decide:
What is the probability that two customers that they will be selected randomly are national people, respectively without a repetition?
P (national customer at 1st time and national customer at the 2nd time).
What is the probability that the customer who will be selected randomly will be under 20 years old, and given he is national, i.e., P (<20 | national)?
If your company has data about the sales achieved during the same year, and the average of sales was 950,000 units with a standard deviation of 102 units, then if the top management asked you to specify which of the sales or revenue data is the most dispersed among the company’s branches?
The following table represents the quantitative data of the scores of 6 auditors regarding their assessment about the performance of two departments within this company: Customer Service and Sales department that are given below.
Department Auditors’ assessment
Accounting 45 53 67 40 35 50
Sales 68 76 70 64 54 66
Calculate the correlation coefficient for these data, and determine the following:
Is there a relationship between the two variables or not?
What is the value and direction of this correlation?
What is the degree of this correlation?
Use software or xls program to analysis and extract your results and interpret it statistically according to the objectives of your organization in order to supporting the decision making optimally
