This document provides information on calculating the median of grouped and ungrouped data. It defines median as the middle value of an ordered data set. For ungrouped odd-sized data, the median is the middle number. For even-sized data, the median is the average of the two middle numbers. For grouped data, the median is calculated by ordering the class boundaries and frequencies, calculating the cumulative frequency, and finding the class where the cumulative frequency equals or exceeds half the total frequency. Several examples are provided to demonstrate calculating the median for different data sets.

1. Midelle Value o 29
me.an of the middle
Class
MEDIAN
i)Ungmuped olata:
.Values/observations a3rangein 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 ofgiven 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 ungaouped 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 ofgivendata
12,14,10,22,19,20.
Ans Ascendingovoder 10,1214),18) 20, 22
th
Medlian( item + L+1 item
2
+1tem
2
37ditem. + 4th item
2
14+18
2
3
Median 16
Median of given data is I6
Trick3
forevenSample.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 ityourselt
EXample Find median of tablet hardness data
obtained 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, 135,14Smg
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 supegvisoas S
Hint:Find out n =2t, Sample sige C) already
in ascendi ng order.
-ccD

4. ) SrmupedData:
I. Adrange values in as cendling 0rder with
uencies)
Their freguencies Ci.e.classec & their freguenri.
generaly these are in,ascending order
2 find out Cumulative freguency
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
etotalfoeouency
2
Ct value in last mw
2
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5. 21
Search for (N )th value in Cumulative
pwr requency column.
Mak that class as Median class.
Lif
Exact valuenot_present in frequencyy
Column Conside nearestnumber (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
PrexiousCf-18
-CC

6. 30
T it your se)
EXample 1 find Mecdian tom the tollowing
cdistibution
40-14h 155-141 1S0s
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 Cless than 0 more than)
O
Cumulative freguency polygon
Vamables
dKCclassboundmes)
On X - aXi1S
Less than method -
UL
More
thanmethod LL
Cumulaive freguency: on - axis
Less than
methool-C.f.in Ting
0Td er.
More than
method F.in ing
OToler
1romy-axis draw hom3ontal
linewhich meets ogive CUe
OR
Considl e (N)th value on
y-axis
-cCD

7. Draw 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'