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Online Tutorial
Math 10
Quarter 4 - Week 1-2
Measures of Position of Ungrouped Data
depedetulay
β’DepED – Cordillera Administrative Region
β’SDO - Camarines Sur
Q4 W2 Math 10
At the end of the session, you will be able to:
β’ calculate a specified measure of position
th
(e.g. 90 percentile) of a set of data; and
β’ solve problems involving measures of
position.
Q4 W2
Math 10
W1 Math
Tukey’s Method
Averina, a shoe store owner, wanted to compare the different brands of
shoes. The table below shows her record of the number of pairs of shoes
bought from each of the brands in one week. Find π1, π2, π3.
107, 128, 137, 138, 141, 142, 151, 209
Mathletes! Are you now ready?
Let’s get started!
#MATHibay
Q4 W2 Math 10
1. It is a measure by which the position of a
data is determined through its value.
a.
quartile
b.
c.
percentile
d. measures of position
Q4 W2 Math 10
decile
2. What measure divides the distribution into
ten equal parts?
a.
quartile
b.
c.
percentile
d. measures of position
Q4 W2 Math 10
decile
3. Which of the following does NOT belong
in the group?
a.
nd
2 quartile
c.
th
5 decile
Q4 W2 Math 10
b.
nd
2 decile
d.
th
50 percentile
MATH I Have Learned
Measures of Position
QUARTILE
DECIILE
PERCENTILE
Divides the distribution
into 4 equal parts
Divides the distribution
into 10 equal parts
Divides the distribution
into 100 equal parts
Ungrouped Data
π
πΈπ = (π + π)
π
Q4 W2 Math 10
π
π«π =
(π + π)
ππ
π
π·π =
(π + π)
πππ
Measures of Position
When the position is in decimal number, we
have two methods in determining the exact
position.
Mendenhall and Sincich Method
Interpolation
Q4 W2 Math 10
Quartiles of Ungrouped Data
3.4
3.6
4
4
ππ%
ππ%
ππ%
πΈπ
πΈπ
πΈπ
ROUND UP
π
πΈπ = (π + π)
π
Q4 W2 Math 10
ROUND DOWN
ππ
π(π + π)
πΈπ =
π
7.4
7.6
7
7
Deciles of Ungrouped Data
10% 20% 30% 40% 50% 60% 70% 80% 90%
π«π π«π π«π π«π π«π π«π π«π π«π π«π
4.3
ROUND UP
5
π
π«π =
(π + π)
ππ
Q4 W2 Math 10
ROUND DOWN
ππ
π(π + π)
π«π =
ππ
8.7
8
Percentiles of Ungrouped Data
10% 20% 30% 40% 50% 60% 70% 80% 90%
π·ππ π·ππ π·ππ π·ππ π·ππ π·ππΆ π·ππ π·ππ π·ππ
2.8
ROUND UP
3
π
π·π =
(π + π)
πππ
Q4 W2 Math 10
ROUND DOWN
ππ
π(π + π)
π·π =
πππ
12.5
12
Quartiles of Ungrouped Data
Calculate the lower quartile(Q1) and upper quartile(Q3) of the
data. The number of days taken by each of 13 employees to finish
a job were 32, 27, 39, 27, 23, 35, 42, 42, 29, 46, 37, 42, and 35.
πΊππππππππ:
1. Arrange the values in ascending order.
23 27 27 29 32 35 35 37 39 42 42 42 46
π
2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π).
π
Note: π is the number of data elements. Thus, π = ππ.
Q4 W2 Math 10
Measures of Position for Ungrouped Data
Mendenhall and Sincich Method
π
2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π).
πΊππππππππ:
π
Note: π is the number of data elements. Thus, π = ππ.
π
πΈπ = (π + π)
π
π
πΈπ = (ππ + π)
π
π
πΈπ = (ππ)
π
πΈπ = π. π
Q4 W2 Math 10
π
πΈπ = (π + π)
π
π
πΈπ = (ππ + π)
π
π
πΈπ = (ππ)
π
πΈπ = ππ. π
Measures of Position for Ungrouped Data
Mendenhall and Sincich Method
π
2. Locate the positions of πΈπ and πΈπ using the formula πΈπ = (π + π).
πΊππππππππ:
π
Note: π is the number of data elements. Thus, π = ππ.
Q4 W2 Math 10
π
πΈπ = (π + π)
π
π
πΈπ = (π + π)
π
πΈπ = π. ππ(ππ + π)
πΈπ = π. ππ(ππ + π)
πΈπ = π. ππ(ππ)
πΈπ = π. ππ(ππ)
πΈπ = π. π
πΈπ = ππ. π
Measures of Position for Ungrouped Data
4π‘β
πΊππππππππ:
10π‘β
23 27 27 29 32 35 35 37 39 42 42 42 46
πΈπ = π. π
πΈπ
πΈπ = ππ. π
ROUND UP
ROUND DOWN
ππ
=π
ππ
πΈπ
πΈπ = ππ
The lower quartile value is the 4th
data element.
The upper quartile value is the 10th
data element.
∴ The value of πΈπ is 29.
∴ The value of πΈπ is 42.
Q4 W2 Math 10
Mendenhall and Sincich Method
Measures of Position for Ungrouped Data
8π‘β
π¬ππππππ:
23 27 27 29 32 35 35 37 39 42 42 42 46
Find the 6th decile of the given data.
π
π«π =
(π + π)
ππ
π
π«π =
(ππ + π)
ππ
ROUND DOWN
π«π = π. ππ(ππ)
The 6th decile value is the 8th data
element.
π«π = π. π
Q4 W2 Math 10
π«π = π
ππ
∴ The value of π«π is 37.
Measures of Position for Ungrouped Data
5π‘β
π¬ππππππ:
23 27 27 29 32 35 35 37 39 42 42 42 46
Find the 32nd percentile of the given data.
π
π·π =
(π + π)
πππ
ππ
π·ππ =
(ππ + π)
πππ
π·ππ = π. ππ(ππ)
π·ππ = π. ππ
Q4 W2 Math 10
ROUND UP
π·ππ = π
ππ
The 32nd percentile value is the 5th
data element.
∴ The value of π·ππ is 32.
Measures of Position for Ungrouped Data
Interpolation
23 27 27 29 32 35 35 37 39 42 42 42 46
πΊπππππππ:
Position of πΈπ = π. π
rd
th
(3.5 falls between 3 and 4 data)
1. Subtract the 3rd data from the 4th data.
ππ − ππ = π
2. Multiply the result by the decimal part obtained in the position of πΈπ .
π. π π = π
3. Add the result in the 3rd data.
π + ππ = ππ
Q4 W2 Math 10
∴ The value of πΈπ using interpolation is 28.
Measures of Position for Ungrouped Data
Interpolation
23 27 27 29 32 35 35 37 39 42 42 42 46
πΊπππππππ:
Position of π«π = π. π
th
th
(8.4 falls between 8 and 9 data)
1. Subtract the 9th data from the 8th data.
ππ − ππ = π
2. Multiply the result by the decimal part obtained in the position of π«π .
π. π π = π. π
3. Add the result in the 8th data.
π. π + ππ = ππ. π
∴ The value of π«π using interpolation is 37.8.
Q4 W2 Math 10
Measures of Position for Ungrouped Data
Interpolation
23 27 27 29 32 35 35 37 39 42 42 42 46
πΊπππππππ:
Position of π·ππ = π. ππ
th
th
(π. ππ falls between 4 and 5 data)
1. Subtract the 4th data from the 5th data.
ππ − ππ = π
2. Multiply the result by the decimal part obtained in the position of π·ππ .
π. ππ π = π. ππ
3. Add the result in the 4th data.
π. ππ + ππ = ππ. ππ
∴ The value of π·ππ using interpolation is 30.44
Q4 W2 Math 10
Mathletes! Are you now ready to
take the Quick Check Challenge
of the Week?
#MATHibay
Q4 W2 Math 10
Mr. Ling is an English teacher. He is interested in the reading speed of his
students. The following are the numbers of words his students can read in one
minute: 50, 25, 23, 30, 42, 20, 13, 16,16, 10, 12, 11, 11, 11, and 19.
10 11 11 11 12 13 16 16 19 20 23 25 30 42 50
1. Find the 1st quartile of the given data.
π
πΈπ = (π + π)
π
π
πΈπ = (ππ + π)
π
π
πΈπ = (ππ)
π
Q4 W2 Math
πΈπ =10π
The 1st quartile value is the 4th data element.
∴ The value of πΈπ is 11.
Mr. Ling is an English teacher. He is interested in the reading speed of his
students. The following are the numbers of words his students can read in one
minute: 50, 25, 23, 30, 42, 20, 13, 16,16, 10, 12, 11, 11, 11, and 19.
10 11 11 11 12 13 16 16 19 20 23 25 30 42 50
2. Find the 8th decile of the given data.
π
π«π =
(π + π)
ππ
π
π«π =
(ππ + π)
ππ
π«π = π. π(ππ)
ππ. π
Q4 W2π«
Math
π = 10
ROUND DOWN
π«π
ππ
= ππ
The 8th decile value is the 12th data element.
∴ The value of π«π is 25.
Measures of Position for Ungrouped Data
3. Find the 8th decile of the given data using interpolation.
10 11 11 11 12 13 16 16 19 20 23 25 30 42 50
Position of π«π = ππ. π
th
th
(12.8 falls between 12 and 13 data)
1. Subtract the 13th data from the 12th data.
ππ − ππ = π
2. Multiply the result by the decimal part obtained in the position of π«π .
π. π π = π
3. Add the result in the 12th data.
π + ππ = ππ
∴ The value of π«π using interpolation is 29.
Mathletes! Are you now ready to
take the Math Challenge of the
Week?
#MATHibay
Q4 W2 Math 10
The scores of Mr. Math Wizard candidate from the five
judges were recorded as follows:
93, 92, 88, 86, and 90.
a. Find π1 , D3, and P10 using Mendenhall and Sincich
Method.
Q4 W2 Math 10
0
