Question

At Colgate-Palmolive Company, the use of descriptive statistics tables and graphs are used to support the quality assurance department in efforts to improve customer satisfaction with detergent products. Propose a similar example from another industry sector and suggest how descriptive statistics tables and graphs would be used to improve customer service or product quality. Be sure to be specific on what data would be used, which table and graph techniques would be used and how the review of these artifacts would be incorporated into the management decision processes. Attach an Excel spreadsheet demonstrating a sample report that could be used to clarify the decision.

Answer 1

ABSTRACT OF THE STUDY:

   Improving student's academic performance is not an easy task for the academic community of higher learning. Descriptive statistics is the discipline of quantitatively describing the main features of a collection of information, or the quantitative description itself. We will be collecting the marks of 100 Students as population and here only marks of 20 students are shown as a sample and apply some measures that can be used like are commonly used to describe a data set. There are different measures of central tendency and measures of variability and dispersion. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness.

SAMPLE DATA:

From a population of 100 students marks, below table shows a sample of 20 students.

CASE	STUDENT'S MARK (20)
1	100
2	85
3	85
4	91
5	94
6	85
7	91
8	85
9	95
10	92
11	85
12	91
13	84
14	92
15	94
16	85
17	95
18	94
19	85
20	85

APPROACH:

(i) UNIVARIATE ANALYSIS:

   We will use Univariate analysis which describes the distribution of a single variable, including its central tendency (including the mean, median, and mode) and dispersion (including data-set, and measures of spread such as the variance and standard deviation). The shape of the distribution may also be described via indices such as skewness and kurtosis.

The characteristics of a variable's distribution may also be depicted in graphical or tabular format, including histograms and stem-and-leaf display.

(ii) BIVARIATE ANALYSIS:

   When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables. In this case, descriptive statistics include:

• Cross-tabulations and contingency tables
• Graphical representation via scatter plots
• Quantitative measures of dependence
• Descriptions of conditional distributions

The main reason for differentiating univariate and bivariate analysis is that bivariate analysis is not only simple descriptive analysis, but it also describes the relationship between two different variables.

ANALYSIS OUTPUT:

HISTOGRAM: Student's Marks Vs Frequency

TABLE 1: MEAN, STANDARD DEVIATION AND NUMBER OF STUDENTS:

Mean	Standard Deviation	N
89.45	4.893	20

TABLE 2: STATISTICAL MEASURES

Mean	89.45
Std. Error of Mean	1.094
Median	88.85
Mode	85
Standard Deviation	4.893
Variance	23.945
Skewness	0.580
Std. Error of Skewness	0.512
Kurtosis	-0.874
Std. Error of Kurtosis	0.992
Range	16
Minimum	84
Maximum	100

RESULT:

   Measures of central tendency includes: the mean is 89.45, median is 88.85 and mode is 85, while measures of variability include: the standard deviation is 4.893 and the variance is 23.945, the minimum is 84 and maximum value of the variables is 100, kurtosis is -0.874 and skewness is 0.580.

CONCLUSION:

In this study, we make use of descriptive statistics in the student's database to predict the student's learning activities. The information generated after the implementation of descriptive statistical technique may be helpful for the instructor as well as for the students. This work may improve student's performance; reduce failing ratio by taking appropriate steps at the right time to improve the quality of education.