Introduction to data distribution management:

Data distribution management is part of statistics.

We receive various data with different frequencies, from different population.

It is our usual practice to compare these data and arrive at a conclusion about the application of these data according to the demand of the situation.

We use certain measures to compare these data. They are called measures of central tendency or averages.

The commonly used averages are mean, median and mode.

Data Distribution Management-arithmetic Mean:-

The common data distribution management is the use of arithmetic mean commonly known as Mean(A.M)

Arithmetic mean = sum of observation/ number of observation = ‘(sumx)/(n)’ where n is the number of observations.

The arithmetic mean is the average of the data distribution. So it is very helpful in data distribution management.

Let us do an example of Arithmetic mean.

The grades scored by 8 students in a test are 45,50,55,60,60,65,70 and 75. Find the mean.

Let us first add all these numbers. 45+50+55+60+60+65+70+75=480

Average or mean or A.M. is ‘(480)/(8)’ = 60 Here ‘Sigma’ X = 480 n= 8 so ‘(sumx)/(n)’ = ‘(480)/(8)’ = 60

The average score of the students is 60

This data distribution management indicates that the students who scored above 60 are above average students

and the students who scored below 60 need to be put in practice to score more grades. This data distribution helps the tutor to identify how much was the intake of the subject by the students. It helps to prepare for future guidance of the student.

When the frequencies are more , the data distribution management uses a formula to arrive at the average.Let us assume 4 students got grade 40 in math, 5 students got 50 and 6 students got 80. Find the mean

we write the above information as x f fx x = number of students

4 40 160 f = frequency of grades

5 50 250 fx = multiplication of f and x

6 80 480

__ ____

total ‘Sigma’x 15 ‘Sigma’fx 900

__ ____

Formula for Mean is ‘(sumfx)/(sumx) ‘= ‘(900)/(15)’ = 60

Data Distribution Management by Use of Median:-

Median is another data distribution management measure. It is the middle value of the data. It divides the data into two equal parts, one part containing less values and the other part containing moe values.

Let us find the median of 20,30,40,50 and 60

There are 5 numbers. The middle number is 40. So median is 40

When you have 6 numbers say 20,30,40,40, 50 60 the median will be average of the two middle numbers.

That is 40+40=80 find ‘(80)/(2)’ = 40 so mdian is 40

The rule is if there are n items and ‘n’ is odd then median is ‘(n+1)/(2)’ th item

If the n numbers are even then median is the mean of ( ‘(n)/(2)’ )th number and [ ‘(n)/(2)’ +1]th number

If there is a discrete frequency distribution then we use a formula .

Median is l +'(N/2 -m)/(f)’ * c where l is the lower limit of the median class, ‘f’ is the frequency of the median class

‘c’ is the width of the class interval and N is the total mof the frequencies.

Let us do a problem grades in math of grade 6 is 50-60 60-70 70-80

frequency 30 40 30

Median class frequency cumulative frequency

50-60 30 30

60-70 40 70 (30+40)

70-80 30 100 (70+30)

N= 100 ‘(N)/(2)’ = ‘(100)/(2)’ = 50

Median class is 60-70(because cf contains 50 in that class only)

l(lower mdian class is 60, f=40 an c =10 (difference in median class) and m is 30 (the previous cf)

so median is = l +'(N/2 -m)/(f)’ * c

=60 + ‘(50 – 30)/(40)’ * 10

=60 +'(20)/(40)*’ 10 = 60 + ‘(1)/(2)’ *10 = 60 + 5 = 65

so median is 65

Data Distribution Management Using Mode:-

The maximum frequency of a data is called mode.

Let us find the mode of the following data : 3,4,5,5,5,5,6,6,7

The frequency of 3 is 1

The frequency of 4 is 1

the frequency of 5 is 4

the frequency of 6 is 2 and

the frequency of 7 is 1

We note frequency of 5 is more .

So mode is 5

If in a 7th grade 40 students scored 50, 50 students scored 60 and 10 students scored 90

the mode is 60 because maximum students scored 60.

Mode is the quickest way of finding the average.

It is the easiest data distrbution management.

Data distribution managerment is used primarily in manufacturing industries, in population studies, in the distribution of allowances to the needy people(public distribution system)