The following table displays the marks obtained by three students on an economics test
Student Marks Obtained (out of 100)
Mary 78
Charles 83
Tony 65
a) Calculate the mean marks obtained by the three students.
b) Suppose one of the scores was reported incorrectly. Charles scored 38 instead of 83. How will the mean change if the correction is incorporated?
c) How does the amount of data used affect the accuracy of a model?
a) The mean, or average, is the sum of the observations in a data set divided by the number of observations. In this case sum of the marks of the three students is 78 + 83 + 65, or 226. Therefore, the average score of the ten students is 226/3, or 75.33.
b) Because one of the scores was wrongly reported, there would be a change in the sum of the scores. If the correct score is considered, the new sum of marks is 226 - 83 + 38, or 181.
Hence, the corrected average score is 181/3, or 60.33.
c) The amount of data used plays an important role in determining the accuracy of a model. A key strength in economic analysis is the amount of data used. Using lots of data, or observations, strengthens the force of an empirical argument and allows the researcher to make more precise statements.
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