ON THE THEORY AND PROCEDURE FOR CONSTRUCTING A MINIMAL-LENGTH, AREA-CONSERVING FREQUENCY POLYGON FROM GROUPED DATA.

THIS PAPER IS CONCERNED WITH GRAPHIC PRESENTATION AND ANALYSIS OF GROUPED OBSERVATIONS. IT PRESENTS A METHOD AND SUPPORTING THEORY FOR THE CONSTRUCTION OF AN AREA-CONSERVING, MINIMAL LENGTH FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM. TRADITIONALLY, THE CONCEPT OF A FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM HAS REFERRED TO THAT POLYGON FORMED BY CONNECTING THE MIDPOINTS OF THE TOPS OF THE RECTANGLES MAKING UP THE HISTOGRAM. THE MOST IMPORTANT DEFICIENCY IN THE TRADITIONAL FREQUENCY POLYGON IS THAT THE AREA OF ANY SPECIFIC RECTANGLE IN THE UNDERLYING HISTOGRAM IS GENERALLY NOT EQUAL TO THE AREA UNDER THE FREQUENCY POLYGON OVER THE SAME INTERVAL. DUE TO THIS DEFICIENCY, DATA ARE SELDOM PRESENTED IN THE FORM OF A FREQUENCY POLYGON. (HW)