This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ercentiles :
The percentile values divide the distribution into 100 parts
each containing 1 percent of the cases. The percentile (Pk) is that
value of the variable up to which lie exactly k% of the total number
of observations.
126 Relationship :
P25 = Q1 ; P50 = D5 = Q2 = Median and P75 = Q3
Percentile for Raw Data or Ungrouped Data :
Example 27:
Calculate P15 for the data given below:
5, 24 , 36 , 12 , 20 , 8
Arranging the given values in the increasing order.
5, 8, 12, 20, 24, 36
th 15(n + 1) P15 = item 100 th 15 × 7 = item 100 = (1.05)th item
= 1st item + 0.05 (2nd item – 1st item)
= 5 + 0.05 (85)
= 5 + 0.15 = 5.15
Percentile for grouped data :
Example 28:
Find P53 for the following frequency distribution.
Class
interval 05 510 1015 1520 2025 2530 3035 3540 Frequency 5 8 12 16 20 10 4 3 Solution:
Class Interval
05
510
1015
1520
2025
2530
3035
3540
Total Frequency
5
8
12
16
20
10
4
3
78
127 C.f
5
13
25
41
61
71
75
78 P53 53N
−m
= l + 100
×c
f
= 20 + 41.34 − 41
×5
20 = 20 + 0.085 = 20.085.
Mode :
The mode refers to that value in a distribution, which
occur most frequently. It is an actual value, which has the highest
concentration of items in and around it.
According to Croxton and Cowden “ The mode of a
distribution is the value at the point around which the items tend to
be most heavily concentrated. It may be regarded at the most
typical of a series of values”.
It shows the centre of concentration of the frequency in around a
given value. Therefore, where the purpose is to know the point of
the highest concentration it is preferred. It is, thus, a positional
measure.
Its importance is very great in marketing studies where a
manager is interested in knowing about the size, which has the
highest concentration of items. For example, in placing an order for
shoes or readymade garments the modal size helps because this
sizes and other sizes around in common demand.
Computation of the mode:
Ungrouped or Raw Data:
For ungrouped data or a...
View
Full
Document
This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

Click to edit the document details