Measurement of position in ungroup data, Quartile

1. Lesson plan in Mathematics Grade 10
Measures of position for ungroup data
January26, 2017
I. Objectives:Atthe endof the lesson75 % of the will be able to:
Illustrate andcalculate the measuresof positionof quartilesinungroupdata.
II. SubjectMatter:Measuresof Positionforungroupdataquartile.
References:Mathematicslearningmodulegrade tenpages362 – 371.
Materials:Manilapaper,Chalk,marker,bondpaper.
Strategies:Interactive Instruction,paircoaching.
ValuesIntegration:Cooperativeness,
III. Procedures:
Teachers Activity Learners Activity
A. Preliminaries
A.1 Prayer
KindlyStandforthe prayerClass
Please leadthe Prayer:Student1.
Good morningClass.
Before youseatdownarrange your seatsand kindlypick
up some piecesof paperson the floor.
A.2 Checkingof Attendance:
Say presentif yourname iscalled.
Let’sbow downour headsand letus
pray.
Amen
Good morningSir.
Presentsir.
B. Review:
C. Motivation:
The shoe sizes of 10 people in a survey are:
8, 9, 9, 7, 10, 6, 7, 8, 9, Me sir.

2. Can anyone findthe medianinthe setdata
Okaystudent1
Correct,
You needtoarrangedit inascendingorderfirst.
6,7,7,8,8,9,9,9,10
So whatis our medianclass
Good classnowthat you foundthe medianourlessonis
justthe continuationof thismedian.
The formulaof findingthe median
sir isfindingthe middlemostno.in
the no. of set sir.
9 sir.
Okaysir.
D. Presentation:
Kindlylookatpage 366 Kindlyread.
A Quartile are the score pointswhichdivide adistribution
intofourequal parts twenty – five percent( 25%) of the
distributionare belowof the firstquartile,fiftypercent (
50%) are belowthe secondquartile,and seventy –five (
75%) are belowthe thirdquartile .Q1 iscalledthe lower
quartile andQ3 is the upperquartile.Q1< Q2<Q3, where
Q2 isnothingbutthe median.The difference betweenQ3
and Q1 is the interquartilerage.
Since the secondquartile isequal tothe median,the steps
incomputationof the medianbyidentifythe medianclass
isthe same as the steps in identifyingthe Q1class andthe
Q3 class.
As yousee inthe pages366
That 25% of the data hasa value of lessthanequal toQ1
and in50% of the data hasa value of lessthanequal to
the medianor Q2 and alsoin 75% of the data has the
value of lessthanequal to Q3.
Example 1.In the book
The ownerof a coffee shophasrecordedthatnumber of
customerswhocame intohis came each hourin a day.
The resultswere 14,10,12, 9, 17, 5,8,9,14,10 and 11. Let’s
findthe lowerquartile andthe upperquartile of the data
,whichmeanswe needtofindthe Q1 and the Q3 .
Solution:
Arranged the data in ascendingorder,itlooklike this.
Yes sir.
Yes sir.
Like inthe medianpatternsir

3. 5, 8,9,9,10,10,11,12,14,14,17.
As youcan see our leastvalue datais5 and the greatest
value datais 17.
Yes class you can us MM
To findthe lowerquartile orthe Q1 is the we needthe
value thatis betweenthe middlevalue andthe leastvalue
inthe data set.
So the lowerquartile is9.
To findthe upperquartile isthe value thatisbetweenthe
middle value andthe greatestvalue inthe dataset.
Sot the upperquartile is14
Othersolution:
In findingthe Q1and Q3
Step1 .Arrangedthe datain ascendingorder
Step2. Use the formula ¼ ( n + 1) = Q1
Step3. Substitute nforthe total no.in a set.
¼ ( 11 + 1) = Q1
3 = Q1
Let count,inthe givenset3 counts
5, 8,9,9,10,10,11,12,14,14,17.
3 counts
So the value of our Q1 = 9
Step4 Letssolve forthe value of Q3.
¾ ( n + 1 ) = Q3
¾ ( 11 + 1 ) = Q3
¾ ( 12 ) = Q3
9 = Q3
Letscount 9 timesfrom5
5, 8,9,9,10,10,11,12,14,14,17.
9 counts
We can use Mata mata sir
What isour answer?
9 countssir.
14 sir isour Q3
Yes Sirsame answers

4. So our Q3 = 14
Didwe have the same answerinour uppersolution.
Mendenhall andSincichmethod
n = no.of elements
LowerQuartile (L) = positionof Q1 = ¼ (n + 1)
Roundup to nearestwhole no.if fallsintwodigitintegers
and
Upper Quartile (U) = Positionof Q3= ¾ ( n + 1)
Rounddownto the nearestwhole no.if fallsintwodigitintegers.
Example.2
In a certaindata set:
( 1,3, 7,7,16,21,27,30,31) and n = 9
to findthe Q1 use the formula:
Positionof Q1= ¼ (n+1 )
¼ (9 + 1)= 2.5 roundup to the nearestwhole integer
whichis3
Positionof Q3 = ¾ ( n + 1)
¾ ( 9 +1) = 7.5 rounddownto the nearestwhole integerwhichis7
Activity1 By pair
Write it ina ¼ piece of paper
Findthe firstquartile Q1,Q2 and Q3 , giventhe scoresof 10
studentsinthe studentsintheirmathematicsactivityusingthe
methodof Mendenhall andSincichMethod.
4,9,7,14,10,8,12,15,6,11
Arrange inascending.
4,6,7,8,9.10,11,12,14,15
Q1 = ¼ ( 10+1)
Q1 = 2.75
Roundup to 3

5. Q1= 3
Q3 = ¾ ( n + 1)
Q3 = 8.25
Rounddownto 8
Q3 = 8
E. Generalization
What isour formulainGettingQ1 andQ3 Class. Q1=1/4 (n + 1 )
Q3 = ¾ ( n + 1)
IV. Evaluation:
Answeritin¼ piece of paper.
Findthe FirstQuartile andthe ThirdQuartile inthe givenscoresof 10 studentsin
mathematicsactivityusingMendenhall andSincichMethod.
10,12,13,14,13,14,15,8,9,7
V. Assignment
Studyinadvance what isan linearInterpolation: