Experiment outcome sample space and event

1
Measures
Of Position
Grouped Data
2
MEASURES OF POSITION

• When data are given in ascending or descending
  order, it can be divided into various parts by
  different values such as Quartiles, Deciles, and
  Percentiles.

3
Lets recall
What are Quartiles? - Divide the distribution
into four equal parts
4
Grouped data are data that have been
bundled/grouped together in categories.

• Histograms and frequency table can be used to
  show this type of data.

5
SCORES FREQUENCY (f)
40-49 6
30-39 9
20-29 2
10-19 3
6
Formula in finding the Quartile values
?? ?? ????( ???? ?? - ???? ?? ?? ???? )
i
7
Wherein
LB lower boundary of the Qk class N total
frequency ???? ?? cumulative frequency of the
class before the Qk class ?? ???? frequency
of the Qk class i size of the class interval k
nth quartile
8
Frequency Distribution Table

• Class Interval

• Frequency

• Lower Boundaries

• Less than Cumulative Frequency

9
Frequency Distribution Table
Class Interval

• are the range of the class and it is denoted as
  small letter i.

10
SCORES
40-49
30-39
20-29
10-19
FREQUENCY (f)
6
9
2
3
FREQUENCY (f)

• is the number of times the data value occurs

N 20
11
Lower Boundaries (LB)
SCORES
40-49
30-39
20-29
10-19
FREQUENCY (f)
6
9
2
4

• The lower boundary of each class is calculated by
  subtracting half of the gap value ½ or 0.5 from
  the class lower limit.

Lower Class limit
12
LESS THAN CUMULATIVE FREQUENCY (ltcf )
LB




SCORES
40-49
30-39
20-29
10-19
f
6
9
2
3
39.5

• it is calculated by adding each frequency from a
  frequency distribution table to the sum of its
  predecessors.

29.5 19.5 9.5
13
SCORES   f LB
40-49 6 39.5
30-39 9 29.5
20-29 2 19.5
10-19 3 9.5
ltcf




14 6 20
59 14
32 5
3
14
SCORES   f LB ltcf
40-49 6 39.5 20
30-39 9 29.5 14
20-29 2 19.5 5
10-19 3 9.5 3
15
Class Scores Intervals Frequency (f) Lower Boundaries (LB) Cummulative Frequency (cf)
41 - 50 7
31 40 21
21 30 16
11 20 12
1 10 4

• N i

16
Class Scores Intervals Frequency (f) Lower Boundaries (LB) Cumulative Frequency (cf)
41 - 50 7 40. 5 60
31 40 21 30.5 53
21 30 16 20. 5 32
11 20 12 10.5 16
1 10 4 0.5 4
N 60 i 10
17
NCAE Scores Frequency Lower Boundaries Cumulative Frequency
24 26 10
21 23 9
18 20 7
15 17 8
12 14 4
9 11 2
6 8 1
3 5 1
N i
18
NCAE Scores Frequency Lower Boundaries Cumulative Frequency
24 26 10 24. 5 42
21 23 9 20 . 5 32
18 20 7 17 . 5 23
15 17 8 14 . 5 16
12 14 4 11 . 5 8
9 11 2 8 . 5 4
6 8 1 5 . 5 2
3 5 1 2 . 5 1
N 42 i 3
19
NCAE Scores Frequency Lower Boundaries Cumulative Frequency
81 90 7
71 80 10
61 70 15
51 60 4
41 50 12
31 40 6
21 30 3
11 20 2
1 - 10 1
N i
20
STEP
BY
STEP
21
Step 1 Construct the Frequency Distribution
Table
22
Step 2 List the value of each element needed
in the formula.
23
Step 3 Solve for the Quartile values using the
formulas
24
Step 4 Substitute then solve for the value of
the given quartile.
25
Step 5 Interpret the value of the quartile.
26
Find the Quartile Values of the given FDT
SCORES   f LB ltcf
40-49 6 39.5 20
30-39 9 29.5 14
20-29 2 19.5 5
10-19 3 9.5 3
27
Calculate the Q1, Q2, and Q3 of the
Mathematics test scores of 50 students.
SCORES FREQUENCY
46-50 4
41-45 8
36-40 11
31-35 9
26-30 12
21-25 6
28
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29
ACTIVITY
Construct the Frequency Distribution Table and
Solve for the Quartile Vales. (On a one whole
sheet of paper).
30
ASSIGNMENT
Solve for the Quartile Values using the table on
(Learners Module Math 10) page 394 , activity 3
(Thats My Place). To be submitted next
meeting on a one whole sheet of paper.