1. STATISTICS

2.  INDIVIDUAL DISCRET CONTINUOUS
S.no Marks Marks Freq. Marks Freq.
1 30 20 8 10 -20 8
2 40 30 12 20 -30 12
3 50 40 20 30 -40 20
4 60 50 10 40 -50 10
5 70 60 6 50 -60 6

3. marks Freq.(f) Cumm.freq.(cf)
20 8 8
30 12 20
40 20 40
50 10 50
60 6 56

4.  Measuresof Central Tendency are used to
describe the set of data.
 Mean
 Median
 Mode



5. 1.Arithmetic Mean
2.Shortcut Method to Mean
3.Direct Method to mean
4.Shortcut Method for Direct Method
5.Calculation of Mean:-
*Individual series
*Discret series
*continuous series

6. Mean
The mean is also known as the average of the set.
Add all of the number is in the set and divide this
sum by the number of items in the set.

7. 1.Easy to understand.
2.Simple to compute.
3. Based on all items.
4.Affected by extreme observation.
5.Capable of further calculation.

8. 1.Arithmetic Mean:
X
X
N
X X1 X 2 X 3 ..... Xn
N =No. of observations/items in a series
x
20
30
10

9.  2. Shortcut method to Mean Ex:-
X d= X-A
d
X A 20
N
Assumed mean 30
 A
d X A 40
50

10.  3.Direct Method:- Marks(X) f fx
f x 20 4
X
f 30 2
40 3
f N
50 1

11.  4.Shortcut Method for Direct Method:-
f d
X A
f
d x A
Marks f d = x-A f.d
20 8
30 12
40 20
50 10

12.  Calculation of Mean in Continuous series:-
f ( m)
X
f
m mid point of class interval
Marks (x) f m f (m)
10 – 20 8
20 – 30 12
30 – 40 20
40 – 50 10
50 - 60 6

13.  Since its definition is precise and clear,
calculation is easy and its value always
determinate.
 Its chief merit consists in the fact that it take
onto consideration every item in the data.
 NO special arrangement of data is necessary
while calculating it, unlike median and mode
where we have to arrange and group the data in
a certain manner.
 It forms a good basis of comparison while
comparing different groups of numerical data.

14.  Omission of even a single item of the data gives an
incorrect value of the A.M., unlike median and mode
where extreme items can simply be discarded.
 It may not identical with any one of the items of the
data. That is, it may not be one of the figures that
comprise the data.
 The fact that it gives a large weight to extreme items
is its handicap since it then fails to be a good
representatives. That is, the value of A.M. of the
data consisting of very and very small items may lead
to wrong conclusions.
 It cannot be used in qualitative studies, unlike the
median.

15. 1.Definition
2.Characteristics
3.Calculating median:-
*Individual series
*Discret series
*Continuous series
4.Advantages & Disadvantages of
median.

16.  The value of the middle item of a series
that is ordered either in the ascending or
descending order of magnitude is called
the median.
1.Measure of central tendency marks order marks order
2.Middle value in ordered
sequence 40 30
 If n is odd, middle 60
value of sequence 20
10
 If n is even, average of 50
2 middle values. (n= no 40
of items in a series) 10 20
30 50

17.  Odd series:- middle value of sequence.(series
must be in order)
 Even series:-
median=
N 1
 th item
2
 N No. of observation

18.  Arrange the data in ascending or descending order
 Find c.f.
 Apply N 1
th
2
 Look for the value in cf. corresponding figure to cf is the median.
Income No. of cf
person(f)
800 16
1000 24
1500 26
1800 30
2000 20
2500 6

19.  Method:- same as discrete series but instead of N 1
2
N
apply 2 to determine the median class.
Then apply,
N
cf
Median = L 2 *i
f
L= lower limit of the median class
cf= cf of the class preciding the median class
f= frequency of median class
i=class interval

20. Marks No.of cf
student(f)
0–5 4 N
2
5 – 10 5
N
10- 15 10 cf
L 2 *i
f
15 – 20 10

21.  Most of the conditions of an ideal average are
satisfied by it.
 The median is of immense use while estimating
qualities such as honestly, intelligence, virtue,
morality etc. and proves to be a good
representative.
 It’s possible to find the median by knowing only
the values of central items and the no. of items.
That is, the values of extreme items are not
necessary for finding the median.

22.  An irregular series is characterized by extreme
variations between the items, in the case of such
a series the median fails to be representative.
 Arrangement of the data either in the ascending
order of the magnitude or descending order is
the chief requisite. This process is tedious when
the data is vast.
 Sometimes the medians may exist between two
values, thus involving the work of estimation.
 Unlike the A.M., it is not possible to find the
total value of all items if we know the value of
the median and the no. of items.

23.  QUARTILE:- It divides the entire series into
4 equal parts.
Quartiles in:-
# Individual & discrete series
# Continuous series

24. N 1
Q1 th
4
N 1
Q3 3 th
4
N N
Q1 th Q3 3 th
4 4
N N
cf 3 cf
4 4
Q1 L *i Q3 L *i
f f

25. Find Q1 & Q3
class f cf
0-5 7
5 – 10 18
10 -15 25
15 – 20 30
20 – 25 20

26. The value of the item in a
variable that is repeated the
greatest number of times is
called the mode.

27. The number that repeats the
most
3, 4, 4, 10, 15, 16, 18
4 is the
mode

28. there may be more than one mode
3, 3, 4, 4, 4, 7, 9, 9, 9
4 & 9 are the modes

29. when there is only single value(f) which is highest.
f1 f 
M L i
2 f1 f  f 2
L= lower limit of model class
f1= frequency of model class
fo= frequency of class preciding the model class
f2= frequency of class successiding the model class

30. Calculate mode
f1 f 
marks No. of M L i
student 2 f1 f  f 2
0 – 10 10
10 – 20 12
20 – 30 15
30 – 40 8
40 - 50 5

31. When there are two similar
frequencies/values which are highest.
MODE = 3 MEDIAN – 2MEAN

32. 1.It is the most predominant item in a
discrete series.
2.If a continuous series is a regular one i.e.
with the maximum frequency in the centre
the mode can be calculated easily without
knowing the frequencies at the two
extremities of the series.
3.It is very useful average in studying business
relating to sales, profits etc.

33. 1.It is quite possible that in certain types of
data it may not be properly defined & hence it
may be indeterminate & indefinite.
2.The value of the mode is not the value
obtained by considering the value of every item
of the data.
3.In the case of an irregular series it is not very
easy to determine the mode.
4.It is quite possible that in certain instances
there may be two or more values for the mode.

34. BOOK:- Quantitative Techniques in
Business by : Dr. Aditham B.Rao