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Name that song…
Here I am
• Holding you, a feeling I never outgrew
Though each and every part of me has tried
Only 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 hand
Nobody can deny that there's something there
• There, running my hands through her hair
Both of us thinking how good it can be
Someone 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 up
To my fifth grade crush, who I thought I really
loved
To the guys I miss, and the girls we kissed
Where are you now?
Where are you now?
Somewhere
• There's a time for us
Someday a time for us
Time together with time to spare
Time to learn
Time to care
Right Here Waiting
• Ocean's apart day after day
And I slowly go insane
I hear your voice on the line
But it doesn't stop the pain
If I see you next to never
How can we say forever
Somewhere down the road
• We had the right love
At the wrong time
Guess I always knew inside
I 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 sumasaya
Lungkot napapawi
Buhay ko'y ngingiti
Sa 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 lilimot
Pusong uhaw sa iyong pag-ibig
Doon Lang
• Kung natapos ko ang aking pag-aaral
Disin sana'y mayron na akong dangal
Na ihaharap sa'yo at ipagyayabang
Sa 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 LM
Relative to the Difficult
Topics/Competencies
Other
Suggestions
(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 1
Measures 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 Statistics
Measures of Central Tendency:
Mean
Median
Mode
Measures of Variability:
Range
Mean deviation
Variance and Standard
Deviation
Descriptive Statistics
Measures of Position:
Quartiles
Deciles
Percentiles
25%
25%
25%
25%
Descriptive Statistics
Measures of Position:
Quartiles
Deciles
Percentiles
Q1
Q2
Q3
First
Quartile
Second
Quartile
Third
Quartile
Descriptive Statistics
Measures of Position:
Quartiles
Deciles
Percentiles
Q3
Q2
Q1
= Median
Quartiles
Q1 (locator):
[0.25(n + 1)]th
Q3
Q2
Q1
25%
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 72
Find the following:
1. Q1
2. Q2
3. Q3
= 19.5
= 40
= 60.5
Measures of Position:
Quartiles
Deciles
Percentiles
D6
D5
D1
= Median
D2
D3
D4
D7
D8
D9
Take note that Dk = P10k
and Pk = Dk/10
Page 371, Activity 6
• Find the quartiles given the scores of 10
students in their Mathematics activity using
Linear Interpolation
• 4 9 7 14 10
• 8 12 15 6 11
4 6 7 8 9 10 11 12 14 15
Q1 :
𝟏
𝟒
(n + 1) =
𝟏
𝟒
(11) = 2. 75
6 7
2 3
Q1 = 6 + .75 (1) = 6 .75
4 6 7 8 9 10 11 12 14 15
Q2 :
𝟐
𝟒
(n + 1) =
𝟏
𝟐
(11) = 5. 5
9 10
5 6
Q2 = 9 + .5 (1) = 9. 5
4 6 7 8 9 10 11 12 14 15
Q3 :
𝟑
𝟒
(n + 1) =
𝟑
𝟒
(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, P65
Class
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
45.5
40.5
35.5
30.5
25.5
20.5
50
46
38
27
18
6
Q1 :
𝟏
𝟒
(50)
Q1 : 𝟏𝟐. 𝟓𝒕𝒉
25.525.5
𝟏𝟐. 𝟓 𝟔
𝟏𝟐
𝟓
= 𝟐𝟖. 𝟐𝟏
D7 :
𝟕
𝟏𝟎
(50)
D7 : 𝟑𝟓𝒕𝒉
25.5
= 𝟑𝟗. 𝟏𝟒
35.5
35 27
11
𝟓
P65 :
𝟔𝟓
𝟏𝟎𝟎
(50)
P65 : 𝟑𝟐. 𝟓𝒕𝒉
25.5
= 𝟑𝟖
𝟑𝟓. 𝟓
𝟑𝟐. 𝟓 𝟐𝟕
𝟏𝟏
𝟓
Act. 6, pp.396-397

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Measures of position

  • 2. Here I am • Holding you, a feeling I never outgrew Though each and every part of me has tried Only you can fill that space inside
  • 3. 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 hand Nobody can deny that there's something there • There, running my hands through her hair Both of us thinking how good it can be Someone is speaking, but she doesn't know he's there
  • 4. I will be here • Tomorrow morning when you wake up and the sun does not appear • I will be here
  • 5. • To my favorite teacher, told me never give up To my fifth grade crush, who I thought I really loved To the guys I miss, and the girls we kissed Where are you now? Where are you now?
  • 6. Somewhere • There's a time for us Someday a time for us Time together with time to spare Time to learn Time to care
  • 7. Right Here Waiting • Ocean's apart day after day And I slowly go insane I hear your voice on the line But it doesn't stop the pain If I see you next to never How can we say forever
  • 8. Somewhere down the road • We had the right love At the wrong time Guess I always knew inside I wouldn't have you for a long time
  • 9. 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?
  • 10. Narito • Minsan pang makita ka Damdamin ay sumasaya Lungkot napapawi Buhay ko'y ngingiti Sa sandaling pag-ibig mo'y makapiling
  • 11. Nandito Ako • Mayro'n akong nais malaman Maaari bang magtanong? Alam mo bang matagal na kitang iniibig? Matagal na akong naghihintay
  • 12. Saan ka man naroroon • Kailan pa man Sa iyo'y lilimot Pusong uhaw sa iyong pag-ibig
  • 13. Doon Lang • Kung natapos ko ang aking pag-aaral Disin sana'y mayron na akong dangal Na ihaharap sa'yo at ipagyayabang Sa panaginip lang ako may pagdiriwang
  • 15. DEPARTMENT OF EDUCATION Topics/ Competencies that are Difficult to Teach or to Learn Remarks/Findings on the Content of TG and LM Relative to the Difficult Topics/Competencies Other Suggestions (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:___________________________
  • 16. Division of Tasks DEPARTMENT OF EDUCATION Groups 1-4 : Module 8 Lesson 1 Measures 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
  • 17. Statistics do not lie, but liars use statistics…
  • 18. Descriptive Statistics Measures of Central Tendency: Mean Median Mode Measures of Variability: Range Mean deviation Variance and Standard Deviation
  • 19. Descriptive Statistics Measures of Position: Quartiles Deciles Percentiles 25% 25% 25% 25%
  • 20. Descriptive Statistics Measures of Position: Quartiles Deciles Percentiles Q1 Q2 Q3 First Quartile Second Quartile Third Quartile
  • 21. Descriptive Statistics Measures of Position: Quartiles Deciles Percentiles Q3 Q2 Q1 = Median
  • 22. Quartiles Q1 (locator): [0.25(n + 1)]th Q3 Q2 Q1 25%
  • 23. Quartiles Q1 (locator): [0.25(n + 1)]th Median/ Q2 (locator): [0.5(n + 1)]th Q3 Q2 Q1 50%
  • 24. 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%
  • 25. Quartiles Example: Given the following data: 11 18 24 33 47 59 61 72 Find the following: 1. Q1 2. Q2 3. Q3 = 19.5 = 40 = 60.5
  • 27. Take note that Dk = P10k and Pk = Dk/10
  • 28.
  • 29. Page 371, Activity 6 • Find the quartiles given the scores of 10 students in their Mathematics activity using Linear Interpolation • 4 9 7 14 10 • 8 12 15 6 11
  • 30. 4 6 7 8 9 10 11 12 14 15 Q1 : 𝟏 𝟒 (n + 1) = 𝟏 𝟒 (11) = 2. 75 6 7 2 3 Q1 = 6 + .75 (1) = 6 .75
  • 31. 4 6 7 8 9 10 11 12 14 15 Q2 : 𝟐 𝟒 (n + 1) = 𝟏 𝟐 (11) = 5. 5 9 10 5 6 Q2 = 9 + .5 (1) = 9. 5
  • 32. 4 6 7 8 9 10 11 12 14 15 Q3 : 𝟑 𝟒 (n + 1) = 𝟑 𝟒 (11) = 8. 25 12 14 8 9 Q3 = 12 + .25 (2) = 12. 5
  • 33. 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
  • 34.
  • 35. 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?
  • 36.
  • 37. Take note that we don’t interpolate for deciles and percentiles.
  • 38. Measures of Position for Grouped Data
  • 40.
  • 41.
  • 42.
  • 43.
  • 45. Find Q1, D7, P65 Class 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 45.5 40.5 35.5 30.5 25.5 20.5 50 46 38 27 18 6
  • 46. Q1 : 𝟏 𝟒 (50) Q1 : 𝟏𝟐. 𝟓𝒕𝒉 25.525.5 𝟏𝟐. 𝟓 𝟔 𝟏𝟐 𝟓 = 𝟐𝟖. 𝟐𝟏
  • 47. D7 : 𝟕 𝟏𝟎 (50) D7 : 𝟑𝟓𝒕𝒉 25.5 = 𝟑𝟗. 𝟏𝟒 35.5 35 27 11 𝟓
  • 48. P65 : 𝟔𝟓 𝟏𝟎𝟎 (50) P65 : 𝟑𝟐. 𝟓𝒕𝒉 25.5 = 𝟑𝟖 𝟑𝟓. 𝟓 𝟑𝟐. 𝟓 𝟐𝟕 𝟏𝟏 𝟓