math ppt rev

2. ONLINE
CLASSROO
M RULES

11. Chinese Zodiac LEGEND
rat ox tiger rabbit dragon snake horse sheep monkey rooster dog pig
Answer the following questions based on the story.
1. Which of the following belongs to the first 50% that arrived earlier than the rest of the group?
A. tiger B. rabbit C. dragon D. all of the above
2. Which of the following belongs to the second 50% that arrived later than the rest of the group?
A. horse B. snake C. dragon D. none of the above
3. Which of the following best represents the median?
A. dragon B. snake C. sheep D. monkey
4. Which of the following belongs to the first 25% that arrived earlier than the rest of the group?
A. tiger B. rabbit C. dragon D. snake
5. How many percent of the animals arrived later than the tiger?
A. 25% B. 50% C. 75% D. 100%

12. MEASURE OF POSITION
It is a measure by which the position of a data is determined through its
value.
Rat ox tiger rabbit dragon snake horse sheep monkey rooster dog pig
A. The tiger belongs to the first 50% or top 50% of the group that arrived earlier than the rest of the
animals.
B. The tiger belongs to the first 25% or top 25% of the group that arrived earlier than the rest of the
animals.
C. The tiger arrived earlier than 75% of the animals.

13. Median is the middlemost value of an arranged
set of data/ distribution.
Example in illustrating a median
•. In a Physical Education class, seven students practiced
shooting the basketball ball from the free throw line for twenty
times. Below is the list of the successful shots done by the seven
students.
9, 3, 5, 6, 8, 10, 11
Find the median of the data set.

14. 9, 3, 5, 6, 8, 10, 11
Solution:
First, let us arrange the values in ascending order:
3, 5, 6, 8, 9, 10, 11
Then, find the middle number.
Since there are 7 values, the middle is the 4th value counting from
either left of right.
3, 5, 6, 8, 9, 10, 11
Therefore, the median is 8.
This means that about 50% of the group has a lower number of
successful shots than 8 and about 50% of the group has a higher
number of successful shots than 8.

15. 3, 5, 6, 8, 9, 10, 11
QUARTILES – are the score points or values which divide a list of ordered numbers into four
equal parts.
– Every distribution has three (3) quartiles
These are the three quartiles denoted as 𝑄1, 𝑄2𝑎𝑛𝑑 𝑄3.
If the data are arranged in ascending order, the second quartile, 𝑄2, is the median of the data set.
This means that 50% of the numbers in the data set lie below 𝑄2.
The first quartile, 𝑄1 is the median of the lower half of the data set. This means that 25% of the
numbers in the data set lie below 𝑄1.
The third quartile, 𝑄3 is the median of the upper half of the data set. This means that 75% of the
numbers in the data set lie below 𝑄3.

16. •This method of illustrating/calculating 𝑄1, 𝑄2 𝑎𝑛𝑑 𝑄3 is called
the Tukey’s Method.
•The quartiles can be interpreted in several ways. For 𝑄1, we can
claim that the pig, dog, and rooster belong to the 25% of the
group that arrived latest in the group.The pig, dog, rooster,
monkey, sheep, horse, snake, dragon, and rabbit belong to the
75% group that arrived later than the rest of the group. Q1, Q2
and Q3 can be interpreted in several ways.
𝑄2
𝑄1 𝑄3
pig dog rooster monkey sheep horse snake dragon rabbit tiger ox rat

17. Activity 2
• Follow the steps to find the different quartile values.
PROBLEM: Eleven students recorded the number of laps of swimming they were able to
do in a twenty-five-meter pool. Below is the number of laps they did.
6, 8, 5, 4, 3, 2, 2, 6, 1, 9, 7
1. Arrange the values in ascending order.
1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 9
2. Identify the median. This is 𝑄2.
𝑄2 = 5
3. Identify the lower half of the values and its median. This is 𝑄1.
𝑄1 = 2
4. Identify the upper half of the values and its median. This is 𝑄3.
𝑄3 = 7

18. Illustrative Examples:
1. The owner of a coffee shop recorded the number of customers who came into his
café each hour in a day. The results were 14, 10, 12, 9, 17, 5, 8, 9, 14, 10 and 11. Find
the lower, middle and upper quartile of the data and interpret results.
Solution:
Arrange in ascending order: 5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17
Determine 𝑄2.
Take the lower half and determine 𝑄1.
Take the upper half and determine 𝑄3.
Interpretation of results.
𝑄1= 9  25% of the number of customers who came to the café is 9 and below.
𝑄2= 10  50% of the number of customers who came to the café is 10 and below.
𝑄3= 14  75% of the number of customers who came to the café is 14 and below.

19. 2. Alice wanted to compare the fruits with high water to substitute
water to hydrate the body and found the following data. Find
𝑄1, 𝑄2 𝑎𝑛𝑑 𝑄3 then interpret results.

20. Solution:
Data in ascending order: 107, 128, 137, 138, 141, 142, 151, 209
Determine 𝑄2.
138+141
2
=
279
2
= 139.5
Take the lower half and determine 𝑄1.
128+137
2
=
265
2
= 132.5
Take the upper half and determine 𝑄3.
142+151
2
=
293
2
= 146.5
Interpretation of results.
𝑄1= 132.5  25% of the fruits has water content of 132.5 mL and below.
𝑄2= 139.5  50% of the fruits has water content of 139.5 mL and below.
𝑄3= 146.5  75% of the fruits has water content of 146.5 mL and below.

21. 3. Albert has an assignment to ask at random 10 students in their school
about their ages. The data are given in the table below. Determine the
values corresponding to 𝑄1 𝑄2 𝑎𝑛𝑑 𝑄3 then interpret results.
Name Age
Ana 10
Ira 13
Susan 14
Antonette 13
Gladys 15
Tony 11
Lito 14
Christian 13
Michael 15
Dennis 12

22. The following are the test scores of 15
students in a 100-item test. Determine
𝑄1, 𝑄2 , 𝑎𝑛𝑑 𝑄3 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑑𝑎𝑡𝑎 𝑠𝑒𝑡.
56, 78, 90, 85, 67, 66, 82, 94, 81, 80, 77,
69, 64, 90, 80
Assessment:

23. Assignment:
•Make a short survey on the number of siblings of
your 12 classmates. Determine the values of
𝑄1, 𝑄2, & 𝑄3 then interpret the results.

24. Mendenhall and Sincich Method
Given a set with n number of
values, first, arrange the data in
ascending order. Next, find the
position of 𝑸𝟏, 𝑳, in the data set:
L = Position of 𝑸𝟏 =
𝟏
𝟒
(𝒏 + 𝟏)
and round UP to the nearest
integer. If L falls halfway
between two integers, ROUND
UP.
Finally, look for the value of the
Lth value in the data set.
To find the position of 𝑸𝟑, 𝒕𝒉𝒆 𝑼,
in the data set, use the formula:
U = Position of 𝑸𝟑 =
𝟑
𝟒
(𝒏 + 𝟏)
and round UP to the nearest
integer. If U falls halfway
between two integers, ROUND
DOWN.
Finally, look for the value of the
Uth value in the data set.

25. Examples:
1. KKD recorded the number of orders
of the different coffee drinks in a day.
CoffeeVariation Number of Orders
Americano 5
Black Coffee 8
Espresso 9
Double Espresso 2
Café Au Lait 10
Latte 5
Macchiato 6
Long Black 7
Cortado 3
A. Arrange the values in ascending
order. 2, 3, 5, 5, 6, 7, 8, 9, 10
B. Locate the position of 𝑸𝟏 using
the formula ¼ (n+1) and ROUND UP
to the nearest integer.
L = position of 𝑸𝟏 = ¼ (9+1) = ¼ (10)
= 2.5
= 3 (rounded up)
= 3rd data
Therefore, 𝑸𝟏= 5

26. C. Locate the position of 𝑸𝟑
using the formula ¾ (n+1)
and round up to the nearest
integer.
U = position of 𝑸𝟑 =
𝟑
𝟒
(9+1) = ¾ (10)
= 7.5
= 7 (rounded down)
= 7th data
Therefore, 𝑸𝟑= 8
2. Albert has an assignment to ask
at random 10 students in their
school about their ages. The data
are given in the table below.
Determine the values corresponding
to 𝑄1, 𝑄2 𝑎𝑛𝑑 𝑄3.

27. Data in ascending order: 10, 11, 12, 13, 13, 13, 14,
14, 15, 15
L=position of 𝑸𝟏 =¼ (10+1) = ¼(11)
= 2.75
= 3
= 3rd data
Therefore, 𝑸𝟏= 12
U=position of 𝑸𝟑 =
𝟑
𝟒
(10+1)=¾ (11)
= 8.25
= 8
= 8th data
Therefore, 𝑸𝟑= 14

28. Deciles - values that divide the data set into 10 equal parts
- there are 9 deciles in each data set
Percentiles – values that divide the data set into 100 equal parts
- there are 99 percentiles in each data set
𝐷
1
𝐷
2 𝐷
3
𝐷
4 𝐷
5
𝐷
6 𝐷
7
𝐷
8
𝐷
9
𝑃
10
𝑃
20
𝑃 30
𝑃
40
𝑃
50
𝑃
60 𝑃
70
𝑃
80
𝑃
90

29. Deciles and percentiles are computed in the same way as
the quartiles. First, arrange the data in ascending order
then, locate the position of the unknown and ROUND UP
to the nearest integer and find the value that corresponds
to the computed position.
Position of 𝑫𝒊 =
𝒊
𝟏𝟎
(𝒏 + 𝟏)
Example:
* Mr. Lupo is an English teacher He is interested in the reading speed of his
students. The following are the number of words his students can read in one
minute.
50 25 23 30 42 20 13 16 16 10 12 11 11 11 19
Find the 7th Decile (𝐷7) and the 60th percentile (𝑃60).
Position of 𝑷𝒊 =
𝒊
𝟏𝟎𝟎
(𝒏 + 𝟏)

30. Data in ascending order:
10 11 11 11 12 13 16 16 19 20 23 25 30 42 50
Position of 𝐷7 =
7
10
(15 + 1)
=
7
10
(16)
=
112
10
= 11.2
The computed value becomes 12 after
rounding up to the nearest integer.
∴ 𝐷7 = 25
70% of the students can read less than or
equal to 25 words per minute and 30% of
the students can read more than or equal
to 25 words per minute.
Position of 𝑃60 =
60
100
(15 + 1)
=
60
100
(16)
=
960
100
= 9.6
The computed value becomes 10 after
rounding up to the nearest integer.
∴ 𝑃60 = 20
70% of the students can read less than
or equal to 25 words per minute and
30% of the students can read more
than or equal to 25 words per minute.