3. Abstract
Keywords
Objectives
Methodology
Introduction
Grouped data
Mean of the grouped data
Ungrouped data
Computation of median for ungrouped data
Conclusion
References
Content
4. Abstract : Grouped and ungrouped data are types of data, however grouped data
has been classified into categories based on similar characteristics whereas
ungrouped data is a raw data. Both types of data can be represented by
frequency tables.
Keywords :
Grouped data : Frequency distribution, summarizing data binning, counts
and bins, multi-dimensional variables.
Ungrouped data: Raw data , categories in numbers ,easily interpret it, easy to
calculate.
Objectives : The main objectives of grouped data is to serve as a convenient
means of summarizing or analysing the data of the frequency distribution. It is
formed by aggregating individual observation of a variables into groups
whereas the main objectives of ungrouped data is the data you first gather from
an experiment or study.
Methodology : This paper contents about secondary resources.
5. The word data refers to information that is collected and recorded. It
can be formed in numbers ,words, measurement and much more.
There are two types of data and these are qualitative and quantitative
data.
When raw data have been grouped in different classes then it is
said to be grouped data.
When the data has not been placed in any categories and no
aggregation/summarization has been taken placed on the data then it
is known as ungrouped data.
Introduction
6. Grouped data are data formed by
aggregating individual observations of a
variables into groups so that a frequency
distribution of the group serves as a convenient
means of summarising or analysing the data.
There are two major types of grouping: data
binning of a single dimensional variables and
multi-dimensional variables.
Grouped data
7. As estimated of the mean of the population from which the data are
drawn can be calculated from the grouped data as:
The mean for the grouped data in the above example, can be
calculated as follows:
Mean of Grouped data
Class intervals Frequenc
y (f)
Midpoint
(x)
FX
5 and above or below 10 1 7.5 7.5
10≤t <15 4 12.5 50
15≤t <20 6 17.5 105
20≤t<25 4 22.5 90
25≤t<30 2 27.5 55
30≤t<35 3 32.5 97.5
20 405
8. Thus, the mean of the grouped data is
The mean for the grouped data in example 4 above can be
calculated as:
Thus, the mean of the grouped data is
Age group Frequency
(f)
Midpoint
(x)
FX
10 10 10.5 105
11 20 11.5 230
12 10 12.5 125
Total 40 460
= 20.25
9. Ungrouped data which is also known as raw data. Raw data is data which
has not been placed in any grouped data or category after collection.
Some of the advantages of ungrouped data are as follows :
I. Most people can easily interpret it.
II. When the sample size is small, it is easy to calculate the mean
median and mode.
III. It does not required technical expertise to analyse it.
Ungrouped data
10. Computation of median for
ungrouped data :
The following two situation could arise;
1. When N is odd. In this case the median can be computed by formula .
Md=the measure or the value of the (N+1)/2-th item.
Score obtain by 7 students on the achievement test be 17,47,15,35,25,39,44.
We have to arrange the score to find out median in ascending or descending
order: 15,17,25,35,39,44,47.4th student i.e, 35 will be the median of the given
score.
2. When N is even, the median is define by given formula.
Md= the value of (N/2) th item +value of [N/2 +1]th item
2
Group of 8 student whose score in a test are 17,47,15,35,25,39,50,44.a
Arranged the scores in ascending series:15,17,25,35,39,44,47,50.
The score of (N/2)th i.e., 4th student=35
The score of [(N/2)+1]th, i.e 5th student =39
Median = 35+39 =37
2
11. Grouping of data helps in improving the
efficiency of estimation and it allows for
greater balancing of statistical power of
test of the different between strata by
analysing equal number from strata.
Whereas ungrouped data it does not
required technical expertise to analyse
it.
Conclusion
