Median - Gropued and Ungrouped Data.pdf

Median Calculation

1. Midelle Value o 29
me.an
of the middle
Class
MEDIAN
i)Ungmuped olata:
.Values/observations a3range in ascending/
descending ovde
2. Count total Number of sample size Cie. n )
3 Tf sample size is odd i.e. n = odol number
L"iHem
Meolian
Codd
Sample
Size)
2
Example: Find Median of given dato
3,8,9,4,12,34,21,7,1.
Ans Ascending o'rder = 1,3,4,7 8),9, 12,21, 34
th em Median item
item
o titem
2
Median
= 5
th ifem
= 08.
. Median of given data is 8
CTick
For oddl sample
size of ung aouped
odlata
median
is always
middlle number.
but data
Should be in ascending or descending ovder.
-CCD

2. 20
4. Tf Sample size 0r items Is even
i.e. n=
even
nunbe
)Hem+ +
Median
CEven
Sample
Si2e) 2
Example: find out median of given data
12,14,10,22,19,20.
Ans Ascending ovoder 10,1214),18) 20,
22
th
Medlian( item + L+1 item
2
+1tem
2
37d item. + 4th item
2
14+18
2
3
Median 16
Median of given data is I6
Trick 3
for even Sample. sige ot ungrDuped data
medidn 1s always mean or average value of
two miolddle numbers but data shouldl be in
ascending or de Scending 0vder.
-@cCD

3. Y
C17y it yourselt
EXample Find median of tablet h ardness data
obtaine d for prmduction
batch .The 0btained
data is 9,5,7,8, 9
and I1
kglcm
CAns: 8 kglom2)
Xample 2: ind median of the disintegration
times
of tablets forr a data set 1,4, 8,3,5, 7,210,
G and 9
min
Ans: 5 5 min)
Example 3: Calculate the median of follouwing
Observartions oF Hb. 0f ftve female
patients.as
l0, 1, 12,
9,9.
CAns: Io Hb7.)
Xample 4 Find Median of following weight ot
Capsules
140,138,130, 150, 135, 14S mg
CAns: 131)
Example 5
Calculate the median salary pald
to
the pmduction supervisor wooking
n
parenteral depamtment
ot phaomaceutical
industny
as per following data
Monthly Salaoy
Cin thousands) (a)
25 26 27 2 8 2
30
31
6
8
20
17
I711
No.0f supeg visoas
S
Hint: Find out n = 2t, Sample sige
C) already
in ascendi ng order.
-ccD

4. ) Srmuped Data:
I. Adrang e
values
in as cendling
0rder with
uencies) Their freguencies Ci.e.class ec
& their freguenri.
generaly
these
are in,a scending order
2 find out Cumulative fre guency
Note
Sf = C.f.,
Value in last row
Median= + N/2-Previous
xh
C.f
f
wheme,
N
= Total number of
observations
i.e. total of toeguencies
= Lower limt of median class
Previous C.f ConsideT Cf of previous f
elass m edian class.
class width CConsider
h
f
frequency of Median class
class interva
in which mecian
ie)
4. Median class
find out
th value of data
etotal foe o uency
2
Ct value in last mw
2
-@cCD

5. 21
Search for ( N )th
value
in Cumulative
pwr requency column.
Mak that class as
Median class.
Lif
Exact value
not_present
in frequencyy
Column
Conside nearest number
(next)
then
Mak that class as
Medicn class
Example:
The daily
expendliture
of 60 Studerts
Of f.4.
B.Phaam is as follows.
Find
out median.
GO 7T0
70-80
90 -q0 0
100 100-120
Daily expense
C)
12 GM14
NO.0f students
Pre
Ans Median-t(N/2 )xh
f
Dauly expense No.0f
Students C.f.
= 90+ (30) X1o
GO-70 8
90t ()x1o
18
1012) 30
0 80
M.C80
80+ 0) X1
0 10o 16
= 80 +10
00 120 460 Me 10
N = f = G0
: 30 e
M.C.
h =
DL-LL= 1o 80
= 10
f = 12
Prexious Cf-18
-CC

6. 30
T
it
y
our se)
EXample 1
find
Mecdian
tom
the tollowing
cdistibution
40-14h
155-141 1S0
s
25
13S-139
130-134
class
freguenc
IS
1S
5
Example 2
find
Median weights
of 500 intats
bovn in a general hosptal
in a single yr
4:0-4
wt.Cin k9)
2.0-2-4 2 S-2
7 30-3: 4 3.s-3.9
132 64
97 No.0f
infants
14
in) Medlian by qraphical
method
Draw oqive
cunre Cle ss
than 0 more than)
O
Cumulative freguency polygon
Vamables
dKCclas s boundmes)
On X -aXi1S
Less than method
-UL
More than method
LL
Cumulaive freguency:
on
-axis
Less than
methool-C.f. in Ting
0Td er.
More than
method F. in ing
OToler
1rom y-axis draw hom3ontal
line which meets ogive CUe
OR
Considl e (N)th value on
y-axis
-cCD

7. Dra w per pendiculas
on
-ax iS
Meeting point
the poit of intes section
Aoives
value of median
2. Draw both ogive cuTVes CLess than+ more t han)
point
of intersection will be
Medican'