Difference between the mean calculated from raw data and from a frequency distribution: a new approach

Abstract

The possible difference between Xbar; computed from the raw data and Xbar; _G calculated from a frequency distribution is an old and, in fact, an irreducible issue because of the rounding of the data. The literature proposes the 95% interval of estimation: where the standard error common length or size of the class intervalsn = total number of data.

Monte Carlo simulations show that the above formula is inappropriate with certain skewed distributions. Based on the shape of the frequency distribution and its smooth, idealized frequency polygon, the “tendency curve”, we propose the alternative formula: , where are the extreme ordinates of the tendency curve.

Keywords:

• Grouped mean
• accuracy
• frequency distribution
• rounding
• histogram

^†Deceased. The surviving authors dedicate this note to the memory of their colleague. We are grateful to Dr. Roger Ward (UQTR) for his help in revising the manuscript. We also wish to thank Mrs. Louise Martin, a colleague and professor at UOTR, for her participation in a preliminary Monte Carlo study bearing on the subject of this paper.

^†Deceased. The surviving authors dedicate this note to the memory of their colleague. We are grateful to Dr. Roger Ward (UQTR) for his help in revising the manuscript. We also wish to thank Mrs. Louise Martin, a colleague and professor at UOTR, for her participation in a preliminary Monte Carlo study bearing on the subject of this paper.

Notes

^†Deceased. The surviving authors dedicate this note to the memory of their colleague. We are grateful to Dr. Roger Ward (UQTR) for his help in revising the manuscript. We also wish to thank Mrs. Louise Martin, a colleague and professor at UOTR, for her participation in a preliminary Monte Carlo study bearing on the subject of this paper.