REPUBLIC OF THE PHILIPPINES
DEPARTMENT OF EDUCATION
REGION XI
DIVISON OF DAVAO CITY
DAVAO CITY
DANIEL R. AGUINALDO NATIONAL HIGH SCHOOL
Matina, Davao City
Name: _______________________________
Date: _______________
Grade and Section: _____________________
Score: _______________
Activity Title: WORKSHEET #1 (4th Quarter): Quartiles for Ungrouped Data using Mendenhall
and Sincich Method.
Example Problem:
There are 12 sections in Grade 10 who qualified for the Scholarship Program offered by NCCC. Listed
below are the number of qualified students in each section.
23
43
56
43
Find each of the following:
23
56
43
23
1) Q1
15
14
38
44
2) Q2
3) Q3
Solution:
a) Arrange the data in ascending order
14
14
15
23
23
23
38
43
43
44
56
56
1
2
3
4
5
6
7
8
9
10
11
12
b) Using Mendenhall and Sincich Method, find the position of
1) Q1
2) Q2
3) Q3
𝒌
(𝒏 + 𝟏)
𝟒
2
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄2 = (12 + 1)
4
2
= (13)
4
= 𝟔. 𝟓𝒕𝒉
*For middle quartile; get the
average of the 6th and 7th
position
6𝑡ℎ + 7𝑡ℎ 23 + 38
=
= 𝟑𝟎. 𝟓
2
2
𝑷𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒐𝒇 𝑸𝒌 =
1
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄1 = (12 + 1)
4
1
= (13)
4
= 𝟑. 𝟐𝟓𝒕𝒉
*For lower quartile; round up
the result
𝟑. 𝟐𝟓 ≈ 𝟒𝒕𝒉 𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
3
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑄3 = (12 + 1)
4
3
= (13)
4
= 𝟗. 𝟕𝟓𝒕𝒉
*For upper quartile; round
down the result
𝟗. 𝟕𝟓 ≈ 𝟗𝒕𝒉 𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
c) Locate the value of the specified quartile
14
14
15
23
23
1
2
3
4
Q1
5
23
38
6
7
Q2 = 30.5
43
43
44
56
56
8
9
Q3
10
11
12
math10worksheet#19_20192020_cvg
Exercises:
Answer the following. Show your solutions. (5 points each)
1)
The number of games won by a famous basketball team each year from the year 1991 to the year 2000
are 20, 25, 20, 45, 35, 50, 35, 45, 30 and 35. Find the difference of the lower quartile and the upper quartile of
the data set.
2)
The rate of an article changed in six consecutive months. Its rate each month was 16, 13, 11, 8, 18, 3.
Find the lower and the middle quartile in the data set.
3)
The owner of a supermarket recorded the number of customers who came into his store each hour in a
day. The results were 11, 7, 9, 6, 14, 2, 5, 6, 11, 7 and 8. Find the lower quartile and upper quartile from the
data.
4)
Annie conducted a math test for her students. The scores they got in the test are 16, 19, 9, 14, 31, 9, 24,
16, 19, 14 and 31. Find the difference between the lower quartile and the middle quartile of the data.
5)
Find the average of the lower, the middle and the upper quartiles of the data. 15, 18, 23, 12, 10, 0, 6, 7,
22 and 12.
math10worksheet#19_20192020_cvg
REPUBLIC OF THE PHILIPPINES
DEPARTMENT OF EDUCATION
REGION XI
DIVISON OF DAVAO CITY
DAVAO CITY
DANIEL R. AGUINALDO NATIONAL HIGH SCHOOL
Matina, Davao City
Name: _____ANSWER KEY!
Date: _______________
Grade and Section: _____________________
Score: _______________
Activity Title: WORKSHEET #1 (4th Quarter): Quartiles for Ungrouped Data using Mendenhall
and Sincich Method.
Exercises:
Answer the following. Show your solutions. (5 points each)
1)
The number of games won by a famous basketball team each year from the year 1991 to the year 2000
are 20, 25, 20, 45, 35, 50, 35, 45, 30 and 35. Find the difference of the lower quartile and the upper quartile of
the data set.
{20, 20, 25, 30, 35, 35, 35, 45, 45, 50}; 𝑛 = 10
1
3
𝑄3 − 𝑄1 = 45 − 25
𝑄1 = (10 + 1)
𝑄3 = (10 + 1)
4
4
= 𝟐𝟎
11
33
=
= 2.75
=
= 8.25
4
4
= 2.75 ≈ 3𝑟𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
= 8.25 ≈ 8𝑡ℎ 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑄1 = 25
𝑄3 = 45
2)
The rate of an article changed in six consecutive months. Its rate each month was 16, 13, 11, 8, 18, 3.
Find the lower and the middle quartile in the data set.
{3,8,11,13,16,18}; 𝑛 = 6
1
2
𝑄1 = (6 + 1)
𝑄2 = (6 + 1)
4
4
7
14
= = 1.75
=
= 3.5
4
4
4𝑡ℎ + 3𝑟𝑑 13 + 11
= 1.75 ≈ 2𝑛𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
=
2
2
𝑸𝟏 = 𝟖
𝑸𝟐 = 𝟏𝟐
3)
The owner of a supermarket recorded the number of customers who came into his store each hour in a
day. The results were 11, 7, 9, 6, 14, 2, 5, 6, 11, 7 and 8. Find the lower quartile and upper quartile from the
data.
{2,5,6,6,7,7,8,9,11,11,14}; 𝑛 = 11
1
3
𝑄1 = (11 + 1)
𝑄3 = (11 + 1)
4
4
12
36
=
=
4
4
= 3𝑟𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
= 9𝑡ℎ 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑸𝟏 = 𝟔
𝑸𝟑 = 𝟏𝟏
math10worksheet#19_20192020_cvg
4)
Annie conducted a math test for her students. The scores they got in the test are 16, 19, 9, 14, 31, 9, 24,
16, 19, 14 and 31. Find the difference between the lower quartile and the middle quartile of the data.
{9,9,14,14,16,16,19,19,24,31,31}; 𝑛 = 11
1
2
𝑄2 − 𝑄1 = 16 − 14
𝑄1 = (11 + 1)
𝑄2 = (11 + 1)
4
4
=𝟐
12
24
=
=
4
4
= 3𝑟𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
= 6𝑡ℎ 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑄1 = 14
𝑄2 = 16
5)
Find the average of the lower, the middle and the upper quartiles of the data. 15, 18, 23, 12, 10, 0, 6, 7,
22 and 12.
{0,6,7,10,12,12,15,18,22,23}; 𝑛 = 10
1
2
3
𝑄1 + 𝑄2 + 𝑄3 7 + 12 + 18
𝑄1 = (10 + 1)
𝑄2 = (10 + 1)
𝑄3 = (10 + 1)
=
4
4
4
3
3
11
22
33
37
=
= 2.75
=
= 5.5
=
= 8.25
=
4
4
4
3
6𝑡ℎ
+
5𝑡ℎ
12
+
12
= 2.75 ≈ 3𝑟𝑑 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
= 8.25 ≈ 8𝑡ℎ 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
=
𝟏𝟐.
𝟑𝟑
=
𝑄1 = 7
𝑄3 = 18
2
2
𝑄2 = 12
math10worksheet#19_20192020_cvg