Quantitative Methods for Business Maths

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Quantitative Methods for Business Maths

Solution

Task 1

a) Histogram

b) Descriptive statistics

Office I
Mean	2,264
Standard Error	0,365425
Median	1,6
Mode	1,48
Standard Deviation	1,634231
Sample Variance	2,670709
Kurtosis	0,766428
Skewness	1,205788
Range	5,79
Minimum	0,53
Maximum	6,32
Sum	45,28
Count	20

1st Quartile = 1.0075

3rdQuartile= 3.0025

Office II
Mean	1,9115
Standard Error	0,406909
Median	1,505
Mode	0,6
Standard Deviation	1,819752
Sample Variance	3,311498
Kurtosis	3,687283
Skewness	1,72485
Range	7,47
Minimum	0,08
Maximum	7,55
Sum	38,23
Count	20

1st Quartile 0.6

3rd Quartile 2.4975

c) Describe the shape

The shape of the histogram of Office 1 can be termed as positively skewed since it has a tail on the right side. Outliers are on the high end of the scale. An outlier is termed as an extreme score in Office 1. This is a score, which lies apart from the rest of distribution. Modality is used in measuring the number of major peaks in a distribution. In office 1 there is only one peak hence uni-modal. A single peak is referred to as uni-modal.

The histogram of Office 2 can be termed as positively skewed since it is right tailed. The histogram also has an outlier since it has an extreme value. It has three peak hence it can be referred to as multimodal.

d) Appropriate Measures of Centrality and Dispersion for the Distribution

Median is a physical center of distribution. Thus, it can be an appropriate measure of dispersion and of centrality since it is not affected by outliers hence appropriate in clearing problems in the central office location. Mode is another measure, which cannot be affected by outliers making it an appropriate measure.

e) Differences Between the Two Central Offices

The two central offices have some differences in their appearance of their histograms, descriptive statistics, and their quartiles. First, looking at the appearance of the two histograms, Office 1 has a uni-modal modality since it has only on peak, while Office 2 has multimodal modality since it has more than two peaks. Second, the two central offices differ in terms of their symmetry since Office 1 is symmetrical, while Office 2 is not symmetrical. Third, the two offices differ in terms of their quartiles because Office 1 quartiles one and three are larger than Office 2.

Fourth, the modes of two central offices differ by a bigger margin since Office 1 has a mode of 1.48, and Office 2 has a mod of 0.6. Fifth, the two offices have some differences in their value, which leads them to have different means. Office 1 is not highly affected by the outliers as compared to Office 2, which has a big difference between the minimum value and the maximum value hence highly affected by the outliers. Sixth, the two offices differ in terms of their distributions. Office 1 has a normal distribution, which is symmetric and uni-modal, while Office 2 does not have a normal distribution, which is multi-modal.

Task 2

Solution

a) The Relationship Between the Type of Job and Gender

There is a strong relationship between types of gender and jobs. This is seen when we look at some jobs like cleaner, which is highly dominated by females. The shelf stacker job is highly dominated by males, which has been the case for a long time that men are good in those technical jobs.

b) Calculation of Probabilities

i) The probability that an employee is female = the total number of women available to work divided by a total number of employees = 97/180 = 0.53889

This means that the probability of a person being female and get employed is high compared to probability of being a male and get employed.

ii) The probability that an employee is male and a checkout operator = number of male employees working as checkout operator divided by a total number of employees working as checkout operator = 10/45 = 0.285714.

This means that a female has a higher probability of being employed as a checkout operator than male.

iii) The probability that an employee is female or a supervisor (or both) = total number of female employees working as supervisors divided by the total number of female employees = 20/97= 0.20619

This means that very few females are ready to work as supervisors.

iv) Given that an employee is male, the probability that he is a shelf stacker = number of male operating as shelf stacker divided by the total number of males = 40/83 = 0.48193

This means that many males prefer operating as shelf operators rather than doing other jobs.

v) Given that an employee is a supervisor, the probability that they are female = the number of female employees working as supervisors divides by the total number of employees working as supervisors = 20/35 = 0.57143

This means that the probability of a female to get a job as a supervisor is high compared to males.

c) Are job category and gender independent or dependent?

Job category and gender are dependent. This means that job category depends on gender. In our case, most of the jobs are operated by females since they do not need any technicality to operate unlike those jobs, which need technical skills, like shelf stacker. In jobs like supervision and checkout operation, a cleaner has a high probability of being operated by female than males i.e. 0.5714 , 0.77778 and 0.64.

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