Measures of Position

1. Good Day
Grade 10

Math
KEITH ADRIAN VILLARAN

2. Let’s have a short
prayer.

3. Prayer

4. Attendance
!!

5. Safety Protocols
Let us promote safe and secure environment. 
• Wear your facemasks always.
• Always wash your hands properly.
• Always sanitize.
• Observe proper distancing.

6. FINDING
MEASURES OF
POSITION

7. MEASURES OF POSITION FOR
UNGROUPED DATA

8. Quartiles
the score points which divide a
distribution into four equal parts

9. Quartiles
a. First Quartile – the value where the twenty-five
percent (25%) of the distribution are below it. It is denoted
by 𝑄1. It is also called as the lower quartile.
b. Second Quartile – the value where fifty percent (50%)
or half of the distribution are below it. It is denoted by 𝑄2
and also the median of the distribution.
c. Third Quartile – the value where seventy-five percent
(75%) of the distribution are below it. It is denoted by 𝑄3.
It is also called as the upper quartile.

10. Quartiles

13. DECILES
the nine score points which divide a
distribution into ten equal parts. They
are denoted as
𝐷1,𝐷2,𝐷3, … ,𝐷9.

14. Find the third decile (𝐷3)
and the seventh decile (𝐷
7) of the distribution:
3, 5, 2, 5, 4, 6, 8, 7, 4.

17. PERCENTILE
The ninety-nine score points
which divide a distribution into one
hundred equal parts.

18. It can be used to determine the values for 1%,
2%, …., and 99% of the distribution. 𝑃40 or 40th
percentile of the distribution means 40% of the
distribution have values less than or equal to 𝑃40.
Finding percentiles is similar to finding quartiles
and deciles except to the formula being used in
finding its positions

22. Types of Permutation
Standard
The equation for
permutation of n
objects taken r at a
time.
01
The different possible
arrangements of
objects in a circle.
Circular
02
the arrangement of a set
of objects where some
of them are alike.
Distinguishable
03
P(n,r) =
𝒏!
(𝒏−𝒓)!
P = (n - 1)! P=
𝒏!
𝒑! 𝒒! 𝒓!….

23. Circular Permutation
Example 2:
How many different arrangements can 4 people be
seated in a circular table?

24. Circular Permutation
P = (n -1)!
Let n = 4
P = 𝟒 − 𝟏 !
P = 3!
P = 3 x 2 x 1
P = 6
6 ways

25. Circular Permutation
For you to try!!
There is a JHS Math Camp in the Division of San
Pablo City held at the oval of Dizon High. Many students
are participating from the different secondary schools.
Each school is asked to form a circle and they will be
sitting on the ground. If the seating arrangement is
circular, in how many possible ways can the 8 members
be seated?

26. Circular Permutation
P = (n -1)!
Let n = 8

27. Circular Permutation
P = (n -1)!
Let n = 8
P = (8 – 1)!
P = 𝟕!
P = 7 x 6 x 5 x 4 x 3 x 2 x 1
P = 5,040
5,040 ways

28. Types of Permutation
Standard
The equation for
permutation of n
objects taken r at a
time.
01
The different possible
arrangements of
objects in a circle.
Circular
02
the arrangement of a set
of objects where some
of them are alike.
Distinguishable
03
P(n,r) =
𝒏!
(𝒏−𝒓)!
P = (n - 1)! P=
𝒏!
𝒑! 𝒒! 𝒓!….

29. Distinguishable Permutation
Example 3:
In how many distinguishable permutations are
possible with the letters of the word CARDONA?

30. Circular Permutation
P =
𝒏!
𝒑! 𝒒! 𝒓!….
CARDONA
There are 7 letters in
the word and 2 A’s are
alike,
therefore, we have:
P =
𝟕!
𝟐!
P =
𝟕 𝒙 𝟔 𝒙 𝟓 𝒙 𝟒 𝒙 𝟑 𝒙 𝟐 𝒙 𝟏
𝟐 𝒙 𝟏
P = 7 x 6 x 5 x 4 x 3
P = 2,520 2,520 ways

31. Distinguishable Permutation
For you to try!!
Find the number of distinguishable permutations in
the word “BOOKS”.

32. Circular Permutation
P =
𝒏!
𝒑! 𝒒! 𝒓!….
BOOKS

33. Circular Permutation
P =
𝒏!
𝒑! 𝒒! 𝒓!….
BOOKS
There are 5 letters in
the word and 2 O’s are
alike,
therefore, we have:
P =
𝟓!
𝟐!
P =
𝟓 𝒙 𝟒 𝒙 𝟑 𝒙 𝟐 𝒙 𝟏
𝟐 𝒙 𝟏
P = 5 x 4 x 3
P = 60 60 ways

34. Permutation
Standard
The equation for
permutation of n
objects taken r at a
time.
0
1
The different possible
arrangements of
objects in a circle.
Circular
02
the arrangement of a set
of objects where some
of them are alike.
Distinguishable
03
P(n,r) =
𝒏!
(𝒏−𝒓)!
P = (n - 1)! P=
𝒏!
𝒑! 𝒒! 𝒓!….
is the arrangement of objects where order matters.

35. ACTIVITY 3.
What to use??
Determine what type of
permutation to be use in
the following problems.

36. 1. Supposed that there are 10 people in the SAN NA ALL Food
Camp. In how many ways can we select an owner, a manager,
and a cashier?
2. Find the number of distinguishable permutations in the word
“CHECK”.
3. In how many ways can 8 people be seated in a circular table?
4. Find the number of distinguishable permutations of the letters in
OHIO.
5. There are 20 students in Educators’ Mathematics Club. In how
many ways can the students be elected as president, vice
president, treasurer, and secretary?
- Standard Permutation
- Distinguishable Permutation
- Circular Permutation
- Distinguishable Permutation
- Standard Permutation

37. 1. Supposed that there are 10 people in the SAN NA ALL Food
Camp. In how many ways can we select an owner, a manager,
and a cashier?
2. Find the number of distinguishable permutations in the word
“CHECK”.
3. In how many ways can 8 people be seated in a circular table?
4. Find the number of distinguishable permutations of the letters in
OHIO.
5. There are 20 students in Educators’ Mathematics Club. In how
many ways can the students be elected as president, vice
president, treasurer, and secretary?

38. ACTIVITY 4.
1. How did you find the activity? Is it easy? Hard?
2. Can we use Permutations in real life situations?
3. Where can we apply Permutations in real life
situations?

39. - Gregory Willis
“Life is full of permutations and
combinations. Sometimes the order you
do things matter, sometimes it doesn’t,
but in order to find the solution in life you
must work through each possibility
presented to find you opportunity.”