Business Report On Quantitative Methods: Data Collection And Analysis

Method of Data Collection

Discuss About The Business Report On Quantitative Methods.

The report is prepared on the basis of a primary data collected by conducting a mini survey using Questionnaire to collect the required data. The purpose of this survey was to collect data on House-hold income expenditure by asking questions to the members of 250 families of a selected urban locality. After collecting the data, a sample of size 20 is drawn by generating random numbers. Then, the required data analysis has been performed to analyse the data based on some selected descriptive statistical measures. This report will help to understand the method of collecting any primary data in practice by preparing statistical questionnaire. It will also ensure to acknowledge a dataset using statistical measures. The statistical measures which have been performed here are the mean, variance, and standard deviation. After that, the confidence intervals are calculated of these estimated parameters at a desired confidence level. management, the required interpretations of these measurements are discussed in the course of this study. All the required calculation has been performed using MS Excel tool. At the end of this report, it recommends how these entire survey could be better and the purpose of the study can be improved (Carlberg 2014).

The study and all the analysis has been done on a primary data. Primary data can be defined as the type of data which is not existing and not readily available on the internet or any journals. To collect this primary data, the personal interview using questionnaire method has been followed. The questionnaire is a list of some questions which are prepared to collect the data for a particular study. The purpose of choosing questionnaire for data collection as the method is quite cheap. Another reason for selecting questionnaire method is to maintain the privacy. Instead of asking the respondents verbally about their incomes, educational qualifications, and expenses, the questionnaire will help to collect the sensitive information without hesitation of the respondents and also to avoid the ignorance of the respondents to answer certain private questions. The questionnaire has been prepared with a combination of eight to ten open-ended and close-ended questions (Pietkiewicz and Smith 2014). In this survey, the researcher personally visited every household, then the questionnaire was given to the member of each household, preferably to the head of the household. The respondents were asked to fill the questionnaire within a stipulated time. Then, the filled questionnaires were collected. The data was collected for the following fields from 250 households-

Data Summary

Household id, Income, Expense for groceries, Expense for Alcohol consumption, Expense for Meals, Cost incurred for Fuel, Cloth, Phone bills, and Utilities, Number of children and adults in the family, Whether the family own a house or not (if “Yes” then it is mentioned by 1; if “No” then it is mentioned by 0), The education level of the head member of the family (“P” stands for Primary, “S” stands for Secondary, “I” for Intermediate, “B” indicates Bachelors, and “M” shows Masters), and lastly, the gender of the head of the household ( “M” for Male, and “F” for Female).

Thus, the size of the population data is 250.

The set of questions, arranged in the Questionnaire are described below:

Q.1. What is the household ID number?

Q.2. What is the total monthly income?

Q.3. What is are expenses incurred for Grocery, Alcohol, Meals, Fuel, Cloth, Phone bills, and    Utilities?

Q.4. How many children are there in the family?

Q.5. What is number of adult members in the family?

Q.6. Whether the Family owns a house? (Mention “Yes” or “No”)

Q.7. What is highest educational qualification possessed by the head of the household/ the earning member of the family? (Indicate “P” for Primary, “S” for Secondary, “I” for Intermediate, “B” for Bachelors, and “M” for Masters)

Q.8. What is the gender of the head of the household? (Indicate “M” for Male, “F” for Female)

It was found that, there were no missing data field, all the respondents have answered all the questions. After the data collection, the random numbers are drawn corresponding to the dataset on the Excel sheet using the Data Analysis Tool Pak. Then, the random numbers are sorted in the ascending order and a sample of size 20 is drawn for further calculation.

The entire dataset has 250 responses on fourteen variables namely- Household ID, Income Grocery, Alcohol, Meals, Fuel, Cloth, Phone, Utilities, Children, Adults, Ownhouse, Highest Degree, and GHH. Among them, there are some categorical or qualitative variables namely, Ownhouse, Highest Degree, and GHH. Rest of the variables are quantitative. From this population, a sample of size 20 is drawn using Simple Random Sampling with Replacement (SRSWR) technique by generating 250 random numbers.

The following image shows the sample of the data.

The sample is analysed using the “Descriptive Statistics” measure from Data Analysis Tool Pak on MS Excel. Here, three numerical variables are selected which are Income, Grocery, and Utilities (Chatfield 2018).

Descriptive Data Analysis

The following tables show the descriptive analysis of the collected data and then the interpretations of the measures.

Income
Mean	68387.2
Standard Error	12831.39
Median	53020.5
Mode	#N/A
Standard Deviation	57383.719
Sample Variance	3292891161.43158
Kurtosis	7.7610453
Skewness	2.6415905
Range	246040
Minimum	21460
Maximum	267500
Sum	1367744
Count	20
Largest(1)	267500
Smallest(1)	21460

The mean value is 68387.2 which is the center of the data. The data points are scattered around this average value. The standard deviation is 57383.719 which indicate that the values of the Income variable are expanded by this value from the mean value. The sample variance is holding a very large value which is 3292891161.43158. The sample variance is a measure of dispersion of the data that is, it is the measurement of the spread of the values from the mean value. A large variance value suggests that values of the Income variable are far from the average as well as from each other.

Grocery
Mean	7260.55
Standard Error	793.510586
Median	6387.5
Mode	5214
Standard Deviation	3548.68722
Sample Variance	12593181
Kurtosis	0.13516015
Skewness	0.67045201
Range	13556
Minimum	2086
Maximum	15642
Sum	145211
Count	20
Largest(1)	15642
Smallest(1)	2086

The center of the data lies at the point 7260.55 as the mean value is 7260.55. The measure of dispersion standard deviation (s.d.) shows the value 3548.687222 and the squared value of the s.d. is the sample variance which holds the value 12593181. Again, the high variance value indicates that the values of the cost for purchasing Grocery items are spread out from one another and they are scattered far away from the mean value.

Utilities
Mean	1192.4
Standard Error	113.0767648
Median	1200
Mode	1200
Standard Deviation	505.6946655
Sample Variance	255727.0947
Kurtosis	0.238286994
Skewness	-0.293928197
Range	2001
Minimum	60
Maximum	2061
Sum	23848
Count	20
Largest(1)	2061
Smallest(1)	60

The mean value is 1192.4, the value of the standard deviation is 505.6946655 and the sample variance is 255727.0947. Like the above two cases, here also the value of the variance is very high, indicating distant position of the values of the cost of utilities variable from the mean value (Wasserman 2013).

The requirement of this paper is to calculate the 95% confidence interval for the population means of the three variables selected previously. 95% confidence interval means that 95% of the time, the interval will contain the population mean.

The confidence interval of population means for each of the three variables – Income, Grocery, and Utilities are calculated using the formula

  ± z ×  ; when the standard deviation is known (Reid, Taylor and Tibshirani 2017).

Here,  = sample mean

z = confidence coefficient which is 1.96 for 95% confidence interval. This coefficient measures the accuracy of the data and it also defines the repetition of the statistical test.

σ = standard deviation

n = sample size. Thus, the lower bound of the confidence interval = ( – z ×  ) and, the upper bound of the confidence interval =   + z × ).

The margin of error can be defined as the quantity (z×). This expression defines the quantity of random sampling error available in the distribution. It indicates the range of values which are above and below of the sample statistic. The margin of error for the confidence interval of population mean is defined by the product of the z-score and (). From the standard normal table, the value of z-score at 95% confidence interval is 1.96.

C.I. for Income
Mean=	68387.2
Standard deviation=	57383.72
Confidence coefficient=	1.96
sample size=	20
Margin of error=	25149.52
Lower bound=	43237.68
Upper bound=	93536.72

Interval Estimation

The 95% confidence interval for the population mean of Income variable is given by (43237.68, 93536.72). It means that there is 95% certainty that the true value of the population mean will lie within that interval calculated interval.

C.I. for Grocery
Mean=	7260.55
Standard deviation=	3548.687
Confidence coefficient=	1.96
sample size=	20
Margin of error=	1555.281
Lower bound=	5705.269
Upper bound=	8815.831

The 95% confidence interval for the population mean of “Grocery” variable is given by (5705.269, 8815.831). It indicates that the chance of the true population mean value to lie within the defined interval is 0.95. The probability of falling the population mean outside this interval is 0.05.

C.I. for Utilities
Mean=	1192.4
Standard deviation=	505.6947
Confidence coefficient=	1.96
sample size=	20
Margin of error=	221.6305
Lower bound=	970.7695
Upper bound=	1414.03

The 95% confidence interval for the population mean of “Utilities” variable is given by (970.7695, 1414.03). There is 95% assurance that the population mean of Utilities variable will fall within the range.

Conclusion

From the above analysis and discussion, it can be concluded that the required key findings of the analysis has been successfully done. Using the MS Excel tool, the measures of location and the measures of dispersion are calculated and interpreted well in the main body of this report. Also, the paper analyses both, the point estimate and the interval estimate. The report aims to provide a quantitative statistical analysis on the basis of a primary dataset. This requirements are met properly in the course of this study. As the dataset contains a primary data, the researcher is more specific about collecting the relevant data based on the purpose of the study and thus, any other bias is not present in the dataset.

The above report only deal with the quantitative variables available in the dataset. Thus, it can be recommended that, the researcher may work with the qualitative or categorical variables of the dataset to draw more detailed interpretation about the data. Besides, the report has so far discussed with the mean, standard deviation, and variance only. The recommended representation of the confidence interval is drawing bar chart and adding error bars on the bar chart. Graphical representation is more helpful to understand the data easily and meaningfully. However, there is enough scope in the course of this paper to analyse other measures of location and other measures of dispersion. The researcher maybe interested to interpret the Median, and Mode of the dataset. Apart from the detailed analysis of the existing data, the researcher may try to collect more elaborate information about the household income expenditure to conduct more extensive analysis on this topic. Another recommendation that can be made is that if the researcher used the secondary data, then the time could be saved that had been wasted for preparing questionnaire, conducting the survey, and collecting the data. Therefore, the secondary would help to save the time of the data. Apart from this, some advanced statistical measures can also be conducted like Regression analysis, taking Income as dependent variable and other options for expenses as independent variables. It will help to predict the income of any house hold if the values of the expense variables are given.

References

Carlberg, C., 2014. Statistical analysis: microsoft excel 2013. Que Publishing.

Chatfield, C., 2018. Statistics for technology: a course in applied statistics. Routledge.

Pietkiewicz, I. and Smith, J.A., 2014. A practical guide to using interpretative phenomenological analysis in qualitative research psychology. Psychological Journal, 20(1), pp.7-14.

Reid, S., Taylor, J. and Tibshirani, R., 2017. Post?selection point and interval estimation of signal sizes in Gaussian samples. Canadian Journal of Statistics, 45(2), pp.128-148.

Wasserman, L., 2013. All of statistics: a concise course in statistical inference. Springer Science & Business Media.