ANIX JEEVANACAHAN

1. INNOVATIVE TEACHING MANUAL
NAME OF THE TEACHER : ANIX JOHNSON STANDARD : IX
NAME OF THE SCHOOL : DIVISION : A
SUBJECT : MATHEMATICS STRENGTH :
UNIT : STATISTICS DURATION : 45 Min
TOPIC : FREQUENCY POLYGON DATE :
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CURRICULAR STATEMENT:
The pupil understands the statistical idea of frequency and the way to construct a frequency polygon of a given data.
CONTENT ANALYSIS:
TERMS: FREQUENCY POLYGON
FACTS:
(i) Statistics is the branch of Mathematics which deals with the organized presentation and
indepth analysis of such data and the methods of drawing logical conclusions from them.

2. (ii) The presentation of numerical data can be done in the form of pictures and tables.
(iii) Numbers used in studying some situation are called scores in Statistics.
(iv) Frequency is the number of times a score is repeated.
(v) The table prepared by using frequencies is called a frequency table.
(vi) A histogram is a graphical representation of a frequency distribution in the form of
rectangles with class intervals as bases and heights proportional to corresponding
frequencies such that there is no gap between any two successive rectangles.
(vii) A frequency polygon is a graphic representation of a given frequency distribution;
obtained by joining the midpoints of the classes of a histogram.
CONCEPT: FREQUENCY POLYGON
PROCESS: Process of making frequency Polygon
LEARNING OUTCOMES:
Enable the students in
(i) comprehending about the preparation of a frequency table.
(ii) constructing frequency polygon with the given data.
PRE-REQUISITES:
The pupils have already learned about

3. (i) Frequency distribution table
(ii) Histogram
TEACHING-LEARNING MATERIALS:
Scale, Pencil etc
Teaching Learning Interaction Procedure
Classroom Interaction Procedure Pupil Response
A[ym]-I≥ Ipim-em-tz-j-W-tØmsS ¢m v Ah-X-cn-∏n-
°p-∂p.
sht°-jv n߃ ASn-®p- s]m-fnt®m?
{In°‰v Ifnt®m?
n߃ Sn.-hn-bn¬ {In°‰v ImWm-dpt- m?
{In°‰v Ifn-bpsS CS-bn¬ Snhn-bn¬ Iptd {Km^p-Iƒ
ImWn-°p-∂Xv n߃ {i≤n-®n-´pt- m?
GsXms° {Km^p-Iƒ BWv ImWn-°p-∂Xv?
ASn-®p-s]m-fn®p
Ifn®p
D- v
D- v
_m¿{Km-^v,- ss]-U-b{Kw

4. NXpcNn{X-ßfpw BhrØn _lp-`p-P-ßfpw I- n-
´pt- m?
At∏mƒ Ωƒ C∂v Cu hnj-b-amWv ]Tn-°p-hm≥
t]mIp-∂-Xv.
A[ym-]-I≥ Bhr-Øn -_-lp-`pPw F∂ hnjbw Ah-X-cn-
∏n-°p-Ibpw AtX-∏-‰n-bp≈ hnh-c-߃ tiJ-cn-°m≥
Bh-iy-s∏-Sp-Ibpw sNøp-∂p.
A[ym-]-I≥ Ip´n-Isf AF∂pw BF∂pw c- m-bn- Xn-cn-
°p-∂p.
A[ym-]-I≥ {Kq∏v AbpsS {]Xn-I-c-W-߃
]cn-tim-[n-°p∂p
A[ym-]-I≥ {Kq∏v BbpsS hnh-c-߃
]cn-tim-[n-°p-∂p.
D- v
Ip´n-Iƒ N¿® sNøp∂p
N¿® sNbvX-Xn-s-∏-‰n-bp≈ hnh-c-߃ tiJ-cn-°m≥ XpS-ßp-
∂p.
A{Kq∏v Xmsg-bp-≈-Xns ]‰n hnh-c-߃ tiJ-cn-°p-∂p.
{Kq∏v B hnhn[ DZm-l-c-W-ß-tfm-Sp-Iq-Snb BhrØn _lp-`p-P-
NXp-c-Nn{Xw
BhrØn _lp-`pPw

5. ASp-Ø-Xmbn A[ym-]-I≥ Hcp tNmZyw ¬Ip-∂p.
"9 A bn¬ ]-Tn-°p∂ 42 Ip´n-I-fpsS ]c--oIvjbpsS
am¿°v Xmsg- X-∂n-cn-°p-∂p. Hmtcm am¿°pw {]tXy-I-am-
bn´v FSpØv Bhr-Øn-]-´nI D- m-°pI'?
A[ym]I≥ AIvsjbvbpsS Ah-X-c-WsØ hne-bn-cp-
Øp-∂p. ¢mknse Ip´n-Iƒ°v BXv F{X-am{Xw {]tbm-P-
-s∏´p F∂pw a- n-em-°p-∂p.
߃ Is- -Øp-∂p.
Cu tNmZy-Øns‚ ASn-ÿm--Øn¬ {Kq∏v Abn¬ n∂v
AIvsjbv BhrØn∏´n-I-sb-°p-dn-®pw, Bhr-Øn-]-´n-I-bpsS
n¿Ωn-Xn-sb-°p-dn®pw ¢mkn¬ Ah-X-cn-∏n-°p-∂p.
F√m Ip´n-Ifpw BhrØn ]´nI Xøm-dm-°p-∂p.
t{KUv Ip´n-Iƒ
4 6
5 5
6 6
7 8
8 9

6. Ip´n-I-fpsS {]h¿Ø-sØ A[ym-]-I≥ hne-bn-cp-Øp-∂p.
A[ym-]-I≥ NXpc Nn{X-ß-sf-∏‰n Ah-X-cn-∏n-°p-∂-Xnv
ASpØ Ah-kcw {Kq∏v Bbnse jmn-Xbv°v ¬Ip∂p
A[ym-]-I≥ DØ-c-߃ ]cn-tim-[n-°p-∂p.
XpS¿∂v BhrØn _lp-`pPw F∂ `mKw Ah-X-cn-∏n-°p-
∂-Xn-mbn as‰mcp Ip´nsb £Wn-°p-∂p.
9 6
10 2
Total 42
jmnX: Iq´p-Im-tc, Ωp-°-dnbmw Ct∏m √ ag-°m-e-amWv
At√?
Ip´n-Iƒ :AtX
jmnX: F∂m¬, hfsc Xm¬]-cyap≈ Hcp tNmZy-Øn-te°v
ap°v IS°mw
Pq¨-˛-Hm-KÃv e`n-°p∂ agsb ASn-ÿm--am°n NXp-c-Nn{Xw hc-
bv°p-I.?
a-g-bpsS Af-hv
Zn-h-k-߃
10-20
8
20-30
10
30-40
14
40-50
20
50-60
15
Ip´n-Iƒ IrXy-ambn hc-bv°p-∂p.

7. A[ym-]-I≥ Nn{Xw ]cn-tim-[n-°p-∂p.
ap≥]-d™ tNmZysØ ap≥n¿Øn {Kq∏v Bbn¬ n∂pw [y
BhrØn _lp-`p-P-Øns‚ n¿ΩmWw hnh-cn-°p-∂p.
[y: Hmtcm NXp-c-Øn-s‚bpw a[y-_nµp AS-bm-f-s∏-SpØn
tbmPn-∏n-°pI.
Hcp- ¢mkv 0-˛10 F∂Xv ]´n-I-bnse H∂m-asØ ¢mknp apºpw
as‰mcp ¢mkv 60----˛70 F∂Xv Ah-km ¢mknp tijhpw
BhrØn ]qPy-ambn AS-bm-f-s∏-Sp-Ø-Ww. Aßs BhrØn
_lp-`pPw n¿Ωn-°m-mhpw.
Ip´n-Iƒ IrXy-ambn hc-bv°p-∂p.
0
5
10
15
20
25
0 20 40 60 80
FREQUENCY POLYGON
DAYS

8. A[ym-]-I≥ Ip´n-Isf A`n--µn-°p-∂p. s]mXp-hmbn
BhrØn _lp-`pPw Fs¥∂v ]d-™p-sIm-Sp-°p-∂p.
¢mkv CS-th-f-I-fpsS a[y-_n-µp-°ƒ tbmPn-∏n®v hc-
bv°p∂ Nn{Xo-I-c-W-amWv BhrØn _lp-`p-Pw.
Ip´n-Iƒ Xs∂ BhrØn _lp-`pPw hc-bv°p-∂Xn-m-h-iy-amb
n¿t±-i-߃ D- m°n ¢mkn¬ {]Z¿in-∏n-°p-∂p.
1. {Km^v t]∏¿ FSp-°p-I. XA£w, YA£w F∂nh hc-
bv°pI. OX,OY AS-bm-f-s∏-Sp-ØpI.
2. X,Y A£-Øn-v¢m-kv, BhrØn F∂nh bYm-{Iaw FSpØv
Bh-iy-amb tXmXv Xnc-s™-Sp-°pI.
3. Hmtcm CS-th-f-bp-tSbpw a[y_nµp AS-bm-f-s∏-Sp-ØpI
4. s]≥knepw skIvbnepw D]tbm-Kn®v t¿tcJ hc®v tbmPn-
∏n-°p-I.

9. Formative Evalution Procedure
Review
1) F¥mWv BhrØn _lp-`pPw?
2) BhrØn _lp-`pPw n¿Ωn-°m-m-hn-iy-amb n¿t±-i-
߃ Fs¥ms°?
Follow Up Activity
Bhr-Øn- _-lp-`pPw Xøm-dm-°pI?
No.of
Days
10-˛20
15
20-˛30
20
30-˛40
14
40-˛50
10
50-˛60
8