Z-Score and Outliers

Following the research, it is expected that the results and the data collected will incorporate outliers in both the data. This may be a result of random errors that are caused by mainly human errors. Several of the data will be beyond twice the standard deviation mean as the reference point. The data furthest from the mean will be evaluated from the data and named as outliers. Usually, the outliers are omitted in the final calculations and conclusion as they can cause erroneous errors. Utilizing the excel spreadsheets, various central tendencies will be determined, including the mean, standard deviation, and later evaluation of the Z-score. An outlier could be below or above the value of the data’s mean as calculated from the raw information recorded. Outliers will also be defined by the use of the Z-score to determine whether the outliers are on the fences for the involved variable.

Correlation and Linear Regression

Referring to part one of the assignment, the relationship that can be conceived from the two variables is that the amount of knowledge in mathematics depends on the hours of studying mathematics. The lower the study hours, the little the amount of knowledge in a given student or respondent. The use of linear regression will be utilized to analyze the involved quantitative variables are mentioned above. The explanatory variable, in this case, will be the hours of studying mathematics, which will be given in hours. For the y-axis, the amount of knowledge in mathematics will serve as it is dependent on the time of the study. Whenever a student spends less time studying, then the likelihood of the student to increase the amount of knowledge in statics is almost zero. The vice versa is predicted and expected to be true.

The level of knowledge is a dependent variable while the hours of study are independent variables, and this is the reason for allocating each into its respective axis. With the quantitative data, different software will be used to record and plot various figures and charts for a better interpretation. A scatterplot will be selected as it works excellent with linear regression in illustrating the strength, form, and direction of the relationship between the variables. The discussion is expected to use the respective terminologies found in statistics. Using an Excel spreadsheet, the correlation will be determined together with the equation for linear regression. The expectation is that there will be a correlation between the observation and the hypothesis formulated. The number of data sources will be less to save time and ensure the accuracy and precision of data and information.

Discussion

The initial belief of the analysis will be confirmed by correlation and linear regression of the variables. The source of data has been streamlined to reduce the chances of errors while maintaining the precision and accuracy of the raw data and consequences of the results found. The presence of outliers affects the precision of data, which might harm overall results. There is a vast range between the mean and the outlier indicating a case of wrongly recording or transferring data creating a drag in the information. Hence, the use of outliers makes the discussion and conclusion invalid and unreliable. The sampling method utilized will be random sampling. This sampling technique involves picking respondents without a strategy. The limitation is that it can be time-consuming, and there might be cases of being biased.