Measures of position

Name that song…

Here I am

• Holding you, a feeling I never outgrewThough each and every part of me has triedOnly you can fill that space inside

Here, there and everywhere• To lead a better life

I need my love to be here• Here, making each day of the year

Changing my life with a wave of her handNobody can deny that there's something there

• There, running my hands through her hairBoth of us thinking how good it can beSomeone is speaking, but she doesn't know he's there

I will be here

• Tomorrow morning when you wake up and the sun does not appear

• I will be here

• To my favorite teacher, told me never give upTo my fifth grade crush, who I thought I really lovedTo the guys I miss, and the girls we kissedWhere are you now?

Where are you now?

Somewhere

• There's a time for usSomeday a time for usTime together with time to spare Time to learn Time to care

Right Here Waiting

• Ocean's apart day after dayAnd I slowly go insaneI hear your voice on the lineBut it doesn't stop the pain

If I see you next to neverHow can we say forever

Somewhere down the road• We had the right love

At the wrong timeGuess I always knew insideI wouldn't have you for a long time

Where is the love?• People killin', people dyin'

Children hurt and you hear them cryin'Can you practice what you preach?Or would you turn the other cheek?

Narito• Minsan pang makita ka

Damdamin ay sumasayaLungkot napapawiBuhay ko'y ngingitiSa sandaling pag-ibig mo'y makapiling

Nandito Ako• Mayro'n akong nais malaman

Maaari bang magtanong?Alam mo bang matagal na kitang iniibig?Matagal na akong naghihintay

Saan ka man naroroon• Kailan pa man

Sa iyo'y lilimotPusong uhaw sa iyong pag-ibig

Doon Lang• Kung natapos ko ang aking pag-aaral

Disin sana'y mayron na akong dangalNa ihaharap sa'yo at ipagyayabangSa panaginip lang ako may pagdiriwang

Measures of Position

Measures of Location

DEPARTMENT OF EDUCATION

Topics/ Competencies

that are Difficult to Teach or to

Learn

Remarks/Findings on the Content of TG and

LMRelative to the Difficult Topics/Competencies

Other Suggestion

s (if any)

ACTIVITY

Directions: Examine the assigned lesson from both LM and TG then fill in the tables below. Present your group output

Module No.____, Lesson No. ____, Topic:___________________________

Division of Tasks

DEPARTMENT OF EDUCATION

Groups 1-4 : Module 8 Lesson 1Measures of Position for Ungrouped

Data, LM, pages 362-382, TG, Pages 322-334

Groups 5-8 : Module 8 Lesson 2 Measures of Position for Grouped Data LM, pages 383-402, TG, Pages 336-359

Statistics do not lie, but liars use statistics…

Descriptive StatisticsMeasures of Central Tendency: Mean Median Mode

Measures of Variability: Range Mean deviation Variance and Standard Deviation

Descriptive Statistics

Measures of Position:QuartilesDecilesPercentiles

25%

25%

25%

25%

Descriptive Statistics

Measures of Position:QuartilesDecilesPercentiles

Q1

Q2

Q3

First Quartile

Second Quartile

Third Quartile

Descriptive Statistics

Measures of Position:QuartilesDecilesPercentiles

Q3

Q2

Q1

= Median

Quartiles

Q1 (locator):

[0.25(n + 1)]thQ3

Q2

Q125%

Quartiles

Q1 (locator):

[0.25(n + 1)]th

Median/ Q2 (locator):

[0.5(n + 1)]th

Q3

Q2

Q1 50%

Quartiles

Q1 (locator):

[0.25(n + 1)]th

Median/ Q2 (locator):

[0.5(n + 1)]th

Q3 (locator):

[0.75(n + 1)]th

Q3

Q2

Q1

75%

Quartiles

Example:Given the following data:11 18 24 33 47 59 61 72Find the following:

1.Q1

2.Q2

3.Q3

= 19.5= 40

= 60.5

Measures of Position:QuartilesDecilesPercentiles

D6

D5

D1

= Median

D2

D3

D4

D7

D8

D9

Take note that Dk = P10k

and Pk = Dk/10

Examples

Page 371, Activity 6

• Find the quartiles given the scores of 10 students in their Mathematics activity using Linear Interpolation

• 4 9 7 1410

• 8 12 15 611

4 6 7 8 9 10 11 12 14 15

Q1 : (n + 1) = (11) = 2. 75

6 7

2 3

Q1 = 6 + .75 (1) = 6 .75

4 6 7 8 9 10 11 12 14 15

Q2 : (n + 1) = (11) = 5. 5

9 10

5 6

Q2 = 9 + .5 (1) = 9. 5

4 6 7 8 9 10 11 12 14 15

Q3 : (n + 1) = (11) = 8. 25

12 14

8 9

Q3 = 12 + .25 (2) = 12. 5

Page 375, Activity 11• Given 50 multiple-choice items in their final test in

Mathematics, the scores of 30 students are the following: • 23 38 28 46 22• 20 18 34 36 35• 45 48 16 22 27• 25 29 31 30 25• 44 21 18 43 21• 26 37 29 13 37• Calculate Q1, Q2, Q3, D2 and D3

Page 377, Activity 12• The scores of Miss World candidates from

seven judges were recorded as follows:• 8.45 9.20 8.56 9.13• 8.67 8.85 9.17• Find the 60th percentile or P60 of the judges’

scores.• What is the P35 of the judges’ scores?

Take note that we don’t interpolate for deciles and percentiles.

Measures of Position for Grouped Data

Prerequisite Skill: Completing the FDT

Find Q1, D3, P40

Find Q1, D7, P65Class

Interval Scores

Freq(f)

Lower Boundaries

(LB)

Less than Cumulative Freq (<cf)

46 -50 4

41 - 45 8

36 - 40 11

31 - 35 9

26 – 30 12

21 – 25 6

45.540.535.530.525.520.5

5046382718

650

Q1 : (50)

Q1 :

25.525.5𝟏𝟐 .𝟓 𝟔

𝟏𝟐𝟓

¿𝟐𝟖 .𝟐𝟏

D7 : (50)

D7 :

25.5¿𝟑𝟗 .𝟏𝟒

35.535 27

11𝟓

P65 : (50)

P65 :

25.5¿𝟑𝟖

𝟑𝟓 .𝟓

𝟑𝟐 .𝟓 𝟐𝟕

𝟏𝟏𝟓

Act. 6, pp.396-397