#NAME 3 MEASURES OF DISPERSIO SERIES#

where Q 1 lies,įq = frequency of the c.i.

upon which Q 3 lies and i = size or length of the c.i. where Q 3 lies,įq = Frequency of the c.i. The Quartile Deviation (Q) is one half the scale distance between the Third Quartile (Q 3) and the First Quartile (Q 1): Quarters are numbered from top to bottom (or from highest score to lowest score), but quartiles are numbered from the bottom to the top. Quarter is a range but quartile is a point on the scale.

Q 3 is the 75th percentile.Ī student must clearly distinguish between a quarter and a quartile. In other words, Q 3 is a point below which 75% of the scores lie.

#NAME 3 MEASURES OF DISPERSIO SERIES#

The value of the item which divides the latter half of the series (with values more than the value of the median) into two equal parts is called the Third Quartile (Q 3) or the Upper Quartile. In other words, it is a point below which 50% of the scores lie. The Second Quartile (Mdn) or the Middle Quartile is the median. In other words, Q 1 is a point below which 25% of cases lie. The value of the item which divides the first half of a series (with values less than the value of the median) into two equal parts is called the First Quartile (Q 1) or the Lower Quartile. The second quartile, or 5th decile or the 50th percentile is the median (see Figure). There are, thus, three quartiles, nine deciles and ninety-nine percentiles in a series. One item divides the series in two parts, three items in four parts (quartiles), nine items in ten parts (deciles), and ninety-nine items in hundred parts (percentiles). Usually, a series is divided in four, ten or hundred parts. However, we should not overlook the fact that range is a crude measure of dispersion and is entirely unsuitable for precise and accurate studies. It is of limited accuracy and should be used with caution. Asymmetrical and symmetrical distribution can have the same range but not the same dispersion. Range does not present the series and dispersion truly. In a class where normally the height of students ranges from 150 cm to 180 cm, if a dwarf, whose height is 90 cm is admitted, the range would shoot up from 90 cm to 180 cm.ĥ. It is affected very greatly by fluctuations in sampling. This is why range is not a reliable measure of variability.Ĥ. Thus a single high score may increase the range from low to high. In group A if a single score 33 (the last score) is changed to 93, the range is widely changed. Just compare the series of scores in group A and group B.

Name 3 measures of dispersio