Abstract Which normal density curve best approximates the sample histogram? The answer suggested here is the normal curve that minimizes the integrated squared deviation between the histogram and the normal curve. A simple computational procedure is described to produce this best-fitting normal density. A few examples are presented to illustrate that this normal curve does indeed provide a visually satisfying fit, one that is better than the traditional , s answer. Some further aspects of this procedure are investigated. In particular it is shown that there is a satisfactory answer that is independent of the bar width of the histogram. It is also noted that this graphical procedure provides highly robust estimates of the sample mean and standard deviation. We demonstrate our technique by using data including Newcomb's data of passage time of light and Fisher's iris data.
[1]
S. Stigler.
Do Robust Estimators Work with Real Data
,
1977
.
[2]
R. Fisher.
THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS
,
1936
.
[3]
David C. Hoaglin,et al.
Applications, basics, and computing of exploratory data analysis
,
1983
.
[4]
D. G. Simpson,et al.
Minimum Hellinger Distance Estimation for the Analysis of Count Data
,
1987
.
[5]
M. Rudemo.
Empirical Choice of Histograms and Kernel Density Estimators
,
1982
.
[6]
J. Tukey,et al.
Transformations Related to the Angular and the Square Root
,
1950
.