Statistics Scaffolding

1. SCAFFOLDING
ASSIGNMENT
HEIDI PALOMO
MATH 1342-M01 ELEMENTARY STATISTICAL
METHODS
FALL 2023

2. Gender pay gap

3. ▪ My opinion, on applying statistics tools over my sample data to draw reasonable conclusions, is that
this will help me collect and analyze data to identify patterns and trends.
▪ I decided to select my sample on 50-60 age range, because I feel it's the age range that has been
working for more years and that has felt a lot more the impact because they have more decades.
▪ The data was collected using the simple random sample method. Data collection was done with a
survey where every selected person will fill out their name, last name, gender, age, occupation, years
of experience, salary, marital status, and if they had children the number of children.
▪ The benefits of using the simple random sample method to collect data are the lack of bias and the
simplicity, and the disadvantages are difficulty gaining access to a list of a larger population, time, costs,
and that bias can still occur under certain circumstances.
▪ I think my data could not be used to draw reasonable conclusions due to samples taken from a
generator. So results would probably not be close to reality.

4. Ethics
▪ Why can’t we use real data for this study?
▪ People may feel ashamed of their earnings and may lied about their income.
▪ Explain the possible ethical issues if instead, you decide to work with data
obtained from real people.
▪ This could have some emotional harm to the participants. For a lot of people
talking about their earnings could be something reallly personal.
▪ Identify possible flaws or biases if data from real people are drawn.
▪ Some data is flawed because the sample of people it surveys doesn't
accurately represent the population. Other data may be flawed because the
researcher only taking samples from a specific income people.

5. Categorizing Variables
Qualitative: characteristics of the
population
Quantitative discrete: Counting whole
numbers
Quantitative Continuous
Gender: It describes the sex of the
population.
Experience: Shows the number of years
the person has been working
Age: How old the person is
Education: It describes the level of
education in words.
Number of children: Number of sons and
daughters the person has
Salary: The amount of money a year
someone generates.
Occupation: Describes the type of job.
Marital status: It describes in words if the
person is single or married.

6. Frequency table and graph
Education Frequency Relative Frequency Percentage
Upper secondary 47 47/200=0.235 23.50%
Master 36 36/200= 0.18 18%
Bachelor 36 36/200= 0.18 18%
Doctoral 31 31/200= 0.155 15.50%
Primary 26 26/200= 0.13 13%
Lower secondary 24 24/200= 0.12 12%
Grand Total 200 200/200= 1 100%
It is evident that the highest frequency of education was upper secondary with 23.50% of the population. The
least is lower secondary with 12% of the population. In the middle we have the master and bachelor with
18% each one, which is a very good level of education. Doctoral which is the highest level of education is
represented by 31 people which is a 15.5% followed by the primary with a 13%. In conclusion more than half
or 50% of the sample population had high level of education or went to college. This means they probably
have a good salary.

7. Discrete Probability Distribution Function
Binomial Distribution Female
P (makes more than $150,000)= 28/112 = 0.25= 25%
X = The number of females with a salary of more than $150,000
x= 0,1,2,3,4,5,6,7,8,9,10
n= number of trials
p= probability of success =0.25
X~B [10,0.25]
Probability that three or less out of ten have a salary less than
$150,000 ?
binomcdf (n,p,x) = binomcdf ( 10, 0.25 ,3) =0.7759
Binomial Distribution Male
P (makes more than $150,000)= 26/88 = 0.2955= 29.55%
X = The number of females with a salary of more than $150,000
x= 0,1,2,3,4,5,6,7,8,9,10
n= number of trials
p= probability of success =0.2955
X~B [10,0.2955]
Probability that three or less out of ten have a salary less than
$150,000 ?
binomcdf (n,p,x) = binomcdf ( 10, 0.2955 ,3) =0.6616

8. Continuous Probability Distribution Function

9. Analysis of my data
▪ According to my data done with the generator, Males with a salary over $150,000
are 26 out of total 88 men. Women that have a salary over $150,000 are 28 out of
112 females. Despite this was done by a random generator, this seems accurate
because in this century a lot of women are working instead of being housewives.
Women are having the same education level or even further than males. I believe
women are growing in education also in the workforce.

10. Metacognition
▪ All probability distributions can be classified as discrete probability distributions
or as continuous probability distributions, depending on whether they define
probabilities associated with discrete variables or continuous variables. A
discrete distribution is one in which the data can only take on certain values, for
example integers. A continuous distribution is one in which data can take on any
value within a specified range which may be infinite. Graphs allow an analyst to
easily spot trends and patterns in data without needing to ask if they are present.
Graphs place the information at an analyst’s disposal; to visualize its form or
structure, to ask the right questions and to draw the right conclusions about the
data at hand. For ease of reading, I will use graphs as a catch-all term that refers
to any visual format of looking at data to support data exploration, analysis,
and/or interpretation. I think the strategy that works best is to have a real
problem that needs a solution. Like this we integrate real data with a context and
purpose. Also, one of the advantages and learning strategies that we have now a
days is technology. I did not know that excel had a function that could help you
with data analysis. This tool facilitates even more the work.