# Quartiles

Quartiles are the measures which divide the data into four equal parts, each portion contains equal number of observations. Thus, there are three quartiles. The first Quartile (denoted by Q1) or lower quartile has 25% of the items of the distribution below it and 75% of the items are greater than it. The second Quartile (denoted by Q2) or median has 50% of items below it and 50% of the observations above it. The third Quartile (denoted by Q3) or upper Quartile has 75% of the items of the distribution below it and 25% of the items above it. Thus, Q1 and Q3 denote the two limits within which central 50% of the data lies.

# Percentiles

Percentiles divide the distribution into hundred equal parts, so you can get 99 dividing positions denoted by P1, P2, P3, ..., P99. P50 is the median value. If you have secured 82 percentile in a management entrance examination, it means that your position is below 18 percent of total candidates appeared in the examination. If a total of one lakh students appeared, where do you stand?

# Calculation of Quartiles

The method for locating the Quartile is same as that of the median in case of individual and discrete series. The value of Q1 and Q3 of an ordered series can be obtained by the following formula where N is the number of observations.
Q1= size of item.
Q3 = size of item.

Example 9
Calculate the value of lower quartile from the data of the marks obtained by ten students in an examination.
22, 26, 14, 30, 18, 11, 35, 41, 12, 32.

Arranging the data in an ascending order,
11, 12, 14, 18, 22, 26, 30, 32, 35, 41.
Q1 = size of = size of item = size of 2.75th item
= 2nd item + .75 (3rd item - 2nd item)
= 12 + .75(14 -12) = 13.5 marks.

Activity
• Find out Q3 yourself.