Set A 11 – Abdella Stats PT
Introduction
We were tasked to interview 20 random Senior High School students in Davao
Doctor’s College and ask their age, height, and weight. Using the data collected we
created three probability mass functions, graphs and calculated the mean and variance
for each data. Moreover, we discussed the implications of these probability mass
functions.
Data Analysis
Age
Age
No. of students
16
4/20
17
11/20
Mean:
M = (0.2)(16) + (0.55)(17) + (0.25)(18)
= 3.2 + 9.35 + 4.5
M = 17.05
Variance:
Var = (0.2)(16)² + (0.55)(17)² + (0.25)(18)² - (17.05)²
= 51.2 + 158.95 + 81 – 290.70
Var = 0.45
Graph:
18
5/20
Implication:
From the mass probability function, it is clear that most of the Senior High School
students we encountered in Davao Doctors College were 17 years old.
Height
Height
in cm
No. of
students
150
152
155
157
163
166
167
170
173
175
185
2
1
2
3
2
1
4
2
1
1
1
Mean:
M = (0.1)(150) + (0.05)(152) + (0.1)(155) + (0.15)(157) + (0.1)(163) + (0.05)(166) +
(0.2)(167) + (0.1)(170) + (0.05)(173) + (0.05)(175) + (0.05)(185)
= 15 + 7.6 + 15.5 + 23.55 + 23.55 + 16.3 + 8.3 + 33.4 + 17 + 8.65 + 8.75 +9.25
M = 163.3
Variance:
Var = (0.1)(150)² + (0.05)(152) ² + (0.1)(155) ² + (0.15)(157) ² + (0.1)(163) ² +
(0.05)(166) ² + (0.2)(167) ² + (0.1)(170) ² + (0.05)(173) ² + (0.05)(175) ² + (0.05)(185)² (163.3)²
= 2,250 + 1,155.2 + 2,402.5 + 3,697.35 + 2,656.9 + 1,377.8 + 5,577.8 + 2,890 +
1,496.45 + 1,531.25 + 1,711.25 – 26,666.89
Var = 79.61
Graph:
Implication:
According to the data collected, the average height of the Senior High School
students we interviewed in Davao Doctor’s College is 167cm. However, there were also
several students with a height of 150cm – 157cm. This is the case since over 40% of
the participants were female.
Weight
Weight
in kg
No. of
students
35
36
39
40
42
43
45
48
49
50
54
62
65
1
1
1
2
1
1
1
1
1
4
2
1
3
Mean:
M = (0.05)(35) + (0.05)(36) + (0.05)(39) + (0.1)(40) + (0.05)(42) + (0.05)(43) + (0.05)(45)
+ (0.05)(48) + (0.05)(49) + (0.2)(50) + (0.1)(54) + (0.05)(62) + (0.15)(65)
= 1.75 + 1.8 + 1.95 + 4 + 2.1 + 2.15 + 2.25 + 2.4 + 2.45 + 10 + 5.4 + 3.1 + 9.75
M = 49.1
Variance:
Var = (0.05)(35)² + (0.05)(36)² + (0.05)(39)² + (0.1)(40)² + (0.05)(42)² + (0.05)(43)² +
(0.05)(45)² + (0.05)(48)² + (0.05)(49)² + (0.2)(50)² + (0.1)(54)² + (0.05)(62)² + (0.15)(65)²
- (49.1)²
Var = 85.99
Graph:
Implication:
Just from looking at the graph we can conclude that most Senior High School
Students from Davao Doctor’s College are more on the lighter side of the scale with
80% of students weighing less than 60kg. Interestingly, shorter students are closer to
being normal weight than taller students.