Mean and standard deviation for open-ended grouped data


Yılmaz A. E., Aktaş Altunay S.

JOURNAL OF POLYTECHNIC-POLITEKNIK DERGISI, vol.25, no.4, pp.1603-1611, 2022 (ESCI)

Abstract

Frequency table of continuous quantitative data is arranged so that to describe the data better and convenience of numerical calculations. There are some difficulties to calculate the descriptive statistics of open-ended grouped data. Because the formulations of mean and standard deviation are based on midpoints, and midpoints are based on class intervals, it is necessary to know the lower-most and upper-most categories. In the previous studies, the interquartile, interdecile, interpercentile, and mid-distance ranges were used to estimate the unknown boundaries. This paper proposes four methods to estimate the population mean and standard deviation in open-ended group data. We conduct an extensive Monte Carlo simulation to compare these methods and the results are discussed over CO2 emission data.