mathematics statistics

2. Quarter 4 Week 3
Ms. Jeraldel Encepto

3. 1. Sort and organize data in
frequency table.
2. Appreciate the importance of
organizing data in frequency
table

4. Gather the birth months of everyone in the
class and organize the data in the table.
Popular Birth Months
Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Number of
Students

5. is a systematic way of presenting
data using a table.
The data are group into different
intervals or number of classes
assigned by the researcher.
Usually, the ideal number of
classes is from 5 to 20 only.

6. Mrs. Abdon a Mathematics Teacher in Rosario National
High School give a long quiz to her students. Given the
set of scores of 60 students in a 50 item test, construct
a frequency distribution table.
34 28 43 21 12 50 26 33 18 28
15 42 33 21 18 17 46 10 13 38
29 30 43 50 23 28 14 31 20 17
23 31 38 32 43 12 18 10 25 19
33 26 24 43 45 30 18 11 23 21
40 48 23 26 34 12 19 24 25 29

7. 1. Choose the number of classes of the
distribution. In the given set of scores,
use 8 as the number of classes or
intervals. (Class interval = 8)
2. Get the range or the difference between
the highest and the lowest values.
Range = highest score – lowest score
= 50 – 10
= 40

8. 3. Solve the class width or class size by
dividing the range by the number of
classes or intervals.
Class size = range = 40 = 5
Class interval 8

9. 4. Use the lowest score as the starting
point if the class size is even. If the
class size is odd, use the multiple of the
class size, which is less than or equal
to the lowest score, as the starting point or
the first lower limit. In the example,
the class size is five and the lowest score
is 10, which is a multiple of class
size. Therefore, you use the lowest score
as the starting point.

10. 5. Determine the next lower limit by adding
the class size.
6. The upper limit of the first interval is
determined by subtracting one from the
second lower value. Repeat the process to
complete the intervals
7. The lower class limit is the lowest value
within the interval, whereas the
upper class limit is the lower class limit and
14 is the upper class limit

11. 8. Get the tally of each score.
9. Determine the corresponding number in
each tally. The number of times
the value appears in the distribution is
called the frequency

12. Frequency is the number of
times an observation or a
particular value appears in a
data set.
A frequency distribution is a
table that shows the frequencies
for the categories, values of a
counting variable or class
intervals.

13. If the observation has fractional measurements such
as height and weight, the following class boundaries
will avoid the gaps between class intervals. For class
interval 16 – 20, the class boundaries are
lower class boundary = 15.5 (subtract 0.5 from 16)
upper class boundary = 20.5 (add 0.5 to 20)
The class interval has class limits; the lower
class limit and the upper class limit. In this
case,
lower class limit = 16
upper class limit = 20.
Class Interval Tally Frequency
16-20 llll-ll 7

14. Each class interval has a class mark.
It is the middle value that may serve as
the representative of the interval. In
this case,
class mark = 18 (since 18 is the
middle score from 16 to 20)
Class
Interval
Class mark Lowe Class
limit
Upper class
limit
Lower class
boundary
Upper class
boundary
16-20 18 16 20 15.5 20.5

15. Tally Column
The Tally column is the record of “sticks” that
gives you the frequency or the number of
values that fall into class interval 16 – 20.
Class
Interval
Class mark Lowe Class
limit
Upper class
limit
Lower class
boundary
Upper class
boundary
16-20 18 16 20 15.5 20.5
Frequency Column
Under the frequency column is the number of
“sticks”. The “slash” serves as the fifth count so
that counting will be easier (IIII is equivalent to 5).
Values or numbers are written in this column.

16. Mrs. Abdon a Mathematics Teacher in Rosario National
High School give a long quiz to her students. Given the
set of scores of 60 students in a 50 item test, construct
a frequency distribution table.
34 28 43 21 12 50 26 33 18 28
15 42 33 21 18 17 46 10 13 38
29 30 43 50 23 28 14 31 20 17
23 31 38 32 43 12 18 10 25 19
33 26 24 43 45 30 18 11 23 21
40 48 23 26 34 12 19 24 25 29

18. Test Scores of 20 students in a 40-item Math quiz
SCORES Tally Frequency
36-40 I 1
31-35 IIII 6
26-30 IIII-IIII 9
21-25 III 3
16-20 II 2

19. Test Scores of 20 students in a 40-item Math quiz
Class
Interval
Class mark Lowe Class
limit
Upper
class limit
Lower
class
boundary
Upper
class
boundary
21-25
SCORES Tally Frequency
36-40 I 1
31-35 IIII 5
26-30 IIII-IIII 9
21-25 III 3
16-20 II 2
Complete the table below for the class interval 21 – 25

20. Jessica is a “Plantita”, she surveyed twenty
households in their barangay and found out the number
of varieties of plants they own. The results are:
3, 0, 1, 4, 4, 1, 2, 0, 2, 2,
0, 2, 0, 1, 3, 1, 2, 1, 1, 3

21. STEP 1: Create a table with 3 columns. Label each
column as: Number of Varieties of plants (Title of the
categories), Tally and Frequency
3 , 0 , 1 , 4 , 4 , 1 , 2 , 0 , 2 , 2 , 0 , 2 , 0 , 1 , 3 , 1 , 2 , 1 , 1 , 3
Number of varieties of
Plants
Tally Frequency

22. STEP 2: Write the categories of the result gathered in
the first column (number of varieties of plants).
3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3, 1, 2, 1, 1, 3
Number of varieties of
Plants
Tally Frequency
0
1
2
3
4

23. STEP 3: Tally the numbers in each category based on
the data gathered in the survey.
3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3, 1, 2, 1, 1, 3
Number of varieties of
Plants
Tally Frequency
0 III
1 IIII-I
2 IIII
3 III
4 II

24. STEP 4: Count the sticks in the tally column and write
the frequency in the third column.
3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3, 1, 2, 1, 1, 3
Number of varieties of
Plants
Tally Frequ5ency
0 III 4
1 IIII-I 6
2 IIII 5
3 III 3
4 II 2

25. STEP 5: Finalize the table. Make sure to write a title.
Frequency Distribution of the Number of Varieties
of Plants of 20 Households
Number of varieties of
Plants
Tally Frequ5ency
0 III 4
1 IIII-I 6
2 IIII 5
3 III 3
4 II 2

26. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
78 96 91 84 87
83 90 79 85 82
92 81 86 85 88
86 89 88 80 76
Consider the following data set.
STEP 1: Find H – Highest score and L – Lowest score
H=
L =

27. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
78 96 91 84 87
83 90 79 85 82
92 81 86 85 88
86 89 88 80 76
Consider the following data set.
STEP 2: Compute for the RANGE, the difference between
the highest and lowest scores.
Let R = H – L

28. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
78 96 91 84 87
83 90 79 85 82
92 81 86 85 88
86 89 88 80 76
Consider the following data set.
STEP 3: If we intend to set the number of class intervals to be
4, then compute for the class size using the formula below.
Class size = 𝑅/4

29. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
Class
Interval
Tally Frequency
96 – 100
91 – 95
86 – 90
81 – 85
76 – 80
Consider the following data set.
STEP 4. Form the table. Complete the list of class intervals.

30. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
Class
Interval
Tally Frequency
96 – 100
91 – 95
86 – 90
81 – 85
76 – 80
Consider the following data set.
STEP 5:Start to complete the TALLY column by marking sticks
where the score falls. You may start at the top left then
across or downward.
78 96 91 84 87
83 90 79 85 82
92 81 86 85 88
86 89 88 80 76

31. Final Math Grades of 20 Grade 7 students (SY 2019-2020)
Class
Interval
Tally Frequency
96 – 100
91 – 95
86 – 90
81 – 85
76 – 80
Consider the following data set.
STEP 6. Lastly, record the total number of sticks per class
interval in the frequency column.
78 96 91 84 87
83 90 79 85 82
92 81 86 85 88
86 89 88 80 76

32. A survey was taken on Costa Verde. In
each of 20 homes, people were
asked how many cars were registered to
their households. The results
were recorded as follows:
1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0

33. A survey was taken on Costa Verde. In
each of 20 homes, people were
asked how many cars were registered to
their households. The results
were recorded as follows:

34. One of the Companies in EPZA are
producing batteries. Thirty AA
batteries were tested to determine how
long they would last. The results,
to the nearest minute, were recorded as
follows:
423, 369, 387, 411, 393, 394,
371, 377, 389, 409, 392, 408,
431, 401, 363, 391, 405, 382,
400, 381, 399, 415, 428, 422,
396, 372, 410, 419, 386, 390

35. One of the
Companies in
EPZA are
producing
batteries.
Thirty AA
batteries
were tested
to determine
how long
they would
last.

36. One of the Grade 7 teachers of Rosario
National High School conduct a
test. Here are the results of the 60 – item
test of a class. Construct a
Frequency distribution
35, 28, 34, 8, 41, 40, 43, 13, 29, 35,
46, 39, 21, 19, 31, 33, 39, 51, 57, 45,
18, 24, 44, 36, 48, 37, 32, 38, 29, 36

38. The following are test scores of Sections
1. Construct a suitable frequency table.
Use intervals of width 6.
14 15 30 19 10 18
26 30 10 15 15 28
10 30 34 40 20 43
20 30 10 22 36 36

39. The following are test scores of Sections
1. Construct a suitable frequency table.
Use intervals of width 6.

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