Quartile

Statistics which divide the observations in a numeric sample into 4 intervals, each containing 25% of the data. The lower, middle, and upper quartiles are computed by ordering the data from smallest to largest and then finding the values below which fall 25%, 50%, and 75% of the data. Thus: * first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile * second quartile (designated Q2) = median = cuts data set in half = 50th percentile * third quartile (designated Q3) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile.

Calculating Quartile

If a data set of values is arranged in ascending order of magnitude, then:

• The median is the middle value of the data set.

  Median = value where n is the number of data values in the data set

• The lower quartile (Q1) is the median of the lower half of the data set.

  value where n is the number of data values in the data set.

• The upper quartile (Q3) is the median of the upper half of the data set.

  value where n is the number of data values in the data set.

Calculation of the Quartiles in a Frequency Distribution

Formulas:

• To calculate the first quartile, Q1 = L + [(1/4N - F1) / f 1] i
• To calculate the second quartile Q2 = L + [(N/2 - F2) / f 2] i
• To calculate the third quartile Q3 = L + [(3/4N - F3) / f 3] i

Notations:

F1 = The cumulative frequency less than up to the class immediately preceding the 1st quartile class. The 1st quartile class is the class which contains Nth/4 item.

F2= The cumulative frequency less than up to the class immediately preceding the median class.

F3 = The cumulative frequency less than up to the class immediately preceding the 3rd quartile class. The 3rd quartile class is the class which contained the 3Nth/4 item.

L = exact lower limit

i = Class-interval of the class in which a particular quartile lies.