Elementary Statistics and Computer Application

Percentiles

• The percentile values divide the distribution into 100 parts each containing 1 percent of the cases. The xth percentile is that value below which x percent of values in the distribution fall. It may be noted that the median is the 50th percentile.

For raw data , first arrange the n observations in increasing order. Then the xth percentile is given by


For a frequency distribution the xth percentile is given by
 


Where

• = lower limit of the percentile calss which contains the xth percentile value (x. n /100)
• = cumulative frequency uotp
• = frequency of the percentile class
• C= class interval
• N= total number of observations

Example 15

• The following are the paddy yields (kg/plot) from 14 plots: 30,32,35,38,40.42,48,49,52,55,58,60,62,and 65 ( after arranging in ascending order). The computation of 25th percentile (Q1) and 75th percentile (Q3) are given below

= 3rd item + (4th item – 3rd item)

= 35 +(38-35)

= 35 + 3 = 37.25 kg


= 11th item + (12th item – 11th item)
= 55 +(58-55)

= 55 + 3 = 55.75 kg

Example 16

The frequency distribution of weights of 190 sorghum ear-heads are given below. Compute 25th percentile and 75th percentile.

 

Weight of ear-heads (in g)	No of ear heads
40-60	6
60-80	28
80-100	35
100-120	55
120-140	30
140-160	15
160-180	12
180-200	9
Total	190

Solution

Weight of ear-heads (in g)	No of ear heads	Less than class	Cumulative frequency
40-60	6	< 60	6
60-80	28	< 80	34
80-100	35	<100	69
100-120	55	<120	124
120-140	30	<140	154
140-160	15	<160	169
160-180	12	<180	181
180-200	9	<200	190
Total	190

For P25, first find out , and for , and proceed as in the case of median.
For P25, we have = 47.5.
The value 47.5 lies between 34 and 69. Therefore , the percentile class is 80-100. Hence,



Similarly,
Class

= 120 +14.33 =134.33 g.