Lesson 1.3: Data Presentation
Learning Activity
Perform as indicated.
1. Given the crime rate in the Philippines from 1981 to 1999 on the table below, construct a
line chart and interpret.
Crime Rate in the Philippines
200
180
178.7
159.9
186.2 184.5
168.1
152.1
160
155.8 157.8
144.6
143.4
140
121.7
120
103.7
88.4
100
80
80.9
63.3
60
56.3 54.2
51.3 50.2
40
20
0
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
Crime Rate
Based on the chart shown above, the crime rate in the Philippines decreases significantly
starting from 1984, although cases of increasing rates emerge from 1888 to 1999, it is not
alarming. Overall, from 1981 to 1999 the crime rates in the Philippines have continued to
show a decreasing rate resulting in less crime rates.
2. The following data represents the height of trees in meters, measured to the nearest tenth
of a sample of 50 trees in a certain region.
4.4
6.6
8.2
4.6
6.5
8.7
6.6
9.8
4.3
5.3
9.8
6.5
7.6
8.8
5.2
5.3
6.5
8.3
6.4
9.4
7.9
6.6
8.8
9.4
6.4
9.9
8.4
7.2
5.8
7.2
6.8
4.7
8.1
9.3
7.5
9.6
5.3
5.9
8.0
6.2
7.3
8.1
9.3
6.5
4.3
4.8
6.4
8.0
9.9
8.7
a. Construct a frequency distribution table
Heights
f
xi
(m)
Class
Relative
Boundaries
Frequency
(RF × 100)
<CFD
>CFD
4.3 – 5.2
7
4.75
4.25 – 5.25
0.14
14
7
50
5.3 – 5.2
6
5.75
5.25 – 6.25
0.12
12
13
43
6.3 – 5.2
13
6.75
6.25 – 7.25
0.26
26
26
37
7.3 – 5.2
9
7.75
7.25 – 8.25
0.18
18
35
24
8.3 – 5.2
6
8.75
8.25 – 9.25
0.12
12
41
15
9.3 – 5.2
9
9.75
9.25 – 10.25
0.18
18
50
9
Total
50
1.00
100
10.25
More
b. Construct the frequency histogram
Histogram
14
Number of Tress
12
10
8
6
4
2
0
4.25
5.25
6.25
7.25
8.25
Heights
Frequency
9.25
Lesson 1.4: Measures of Location
Learning Activity
Perform as indicated.
Suppose we are interested in describing the average monthly high
temperatures (℃) for 2019 in Manila, Philippines: 29.5, 30.2, 31.9, 33.3, 33.4,
32.1, 31.2, 30.4, 30.6, 30.9, 30.5, 29.6. (Note: Since 2019 is the year of interest,
these 12 values already comprise the population of interest.)
Find the following and interpret: mean, median, mode, first quartile, and third quartile.
Mean:
∑𝑁
373.6
𝑖=1 𝑋𝑖
=
≅ 31.13
𝑁
12
𝜇=
From the result, we can say that most of the values from the average monthly high
temperatures are close to 31.13.
Median:
𝜇̃ =
29.5, 29.6, 30.2, 30.4, 30.5, 30.6, 30.9, 31.2, 31.9, 32.1, 33.3, 33.4
𝑥(𝑛) + 𝑥(𝑛+1)
2
2
2
=
𝑥(12) + 𝑥(12+1)
2
2
2
=
𝑥6 + 𝑥7 30.6 + 30.9 61.5
=
=
= 30.75
2
2
2
As we can observe, since the n of the said population is even, the middle value is taken from
the two respective middle values of the population, resulting in a median of 30.75.
Mode:
No mode
First Quartile:
𝑄1 =
𝑛𝑖 (12)(1)
=
=3
4
4
𝑥 𝑛𝑖 + 𝑥 𝑛𝑖
𝑄1 =
(
4
)
(
4
+1)
2
𝑥 (12)(1) + 𝑥 (12)(1)
(
=
4
)
(
4
+1)
=
2
𝑥3 + 𝑥4 30.2 + 30.4 60.6
=
=
= 30.3
2
2
2
Based on the result, 25% of the average monthly high temperatures (℃) for 2019 in Manila,
Philippines is less than 30.3.
Third Quartile:
𝑄1 =
𝑛𝑖 (12)(3)
=
=9
4
4
𝑥 𝑛𝑖 + 𝑥 𝑛𝑖
𝑄1 =
(
4
)
(
2
4
+1)
𝑥 (12)(3) + 𝑥 (12)(3)
(
=
4
)
(
2
4
+1)
=
𝑥9 + 𝑥10 31.9 + 32.1 64
=
=
= 32
2
2
2
The third quartile indicates that at least 75% of the average monthly high temperatures (℃)
for 2019 in Manila, Philippines is less than 32, while 30% is greater than 32.