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Biblioteka

1.2 Data, Sampling, and Variation in Data and Sampling (4/21/2025)

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Posljednje ažuriranje about 1 year ago
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Untitled Section 1
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Examples
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Qualitative Data Discussion
Omitting Categories/Missing Data

The table displays Ethnicity of Students but is missing the "Other/Unknown" category. This category contains people who did not feel they fit into any of the ethnicity categories or declined to respond. Notice that the frequencies do not add up to the total number of students. In this situation, create a bar graph and not a pie chart.

Pie Chart: No Missing Data

Sampling

Non Random Sampling example

Convenience sampling involves using results that are readily available. (only interviewing people that are easily accessible)

Sampling with replacement is truly random sampling (there is a chance to be selected more than once). However, most studies do a random sample without replacement for practical reasons.

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Examples
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Sample Size
Variation
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Homework

Classwork 53-79 odd

https://openstax.org/books/introductory-statistics-2e/pages/1-homework

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Pitanje 1
1.

Given the definitions of Qualitative and Quantitative make an educated guess where these would be placed

Qualitative data are the result of categorizing or describing attributes of a population.

Quantitative data are the result of counting or measuring attributes of a population.

Hair Color

Blood Type

Jersey Number

The data are the weights of backpacks with books in them. You sample the same five students. The weights (in pounds) of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different weights.

The data are the areas of lawns in square feet. You sample five houses. The areas of the lawns are 144 sq. feet, 160 sq. feet, 190 sq. feet, 180 sq. feet, and 210 sq. feet. What type of data is this?

The data are the number of machines in a gym. You sample five gyms. One gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines.

b. The type of car you drive

d. The number of classes you take per school year

f. Weights of dogs at an animal shelter

h .A statistics professor collects information about the classification of her students as first-year students, sophomores, juniors, or seniors.

Below are tables comparing the number of part-time and full-time students at De Anza College and Foothill College enrolled for the most recent spring quarter. The tables display counts (frequencies) and percentages or proportions (relative frequencies). The percent columns make comparing the same categories in the colleges easier. Displaying percentages along with the numbers is often helpful, but it is particularly important when comparing sets of data that do not have the same totals, such as the total enrollments for both colleges in this example. Notice how much larger the percentage for part-time students at Foothill College is compared to De Anza College.

Tables are a good way of organizing and displaying data. But graphs can be even more helpful in understanding the data. There are no strict rules concerning which graphs to use. Two graphs that are used to display qualitative data are pie charts and bar graphs.

In a pie chart, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category.

In a bar graph, the length of the bar for each category is proportional to the number or percent of individuals in each category. Bars may be vertical or horizontal.

A Pareto chart consists of bars that are sorted into order by category size (largest to smallest).

Percentages That Add to More (or Less) Than 100%

Sometimes percentages add up to be more than 100% (or less than 100%). In the graph, the percentages add to more than 100% because students can be in more than one category. A bar graph is appropriate to compare the relative size of the categories. A pie chart cannot be used. It also could not be used if the percentages added to less than 100%.

A sample should have the same characteristics as the population it is representing

Must be a Random Sample

Example is Simple Random Sampling- Each group of size n is likely to be chosen as another group of size n. Examples, pulling names out of a hat, or generating random numbers on a computer to select people

Stratified Sample- Divide the population into groups and take a proportionate simple random sample of each. (ie pick three random students from each classroom)

Cluster Sample- Divide the population into clusters, and randomly select some of the clusters. (ie pick 6 random classrooms and get information from all students)

Systematic Sample- Randomly select a starting point and take every nth piece of data from a listing of the population. (Use student ID's and select every ten students for study)

Sampling Error the process in which the sampling mistakes occur, like not having a large enough sample

Non- Sampling Errors- Things not to do with sampling mistakes like a faulty machine or bad record keeping.

Sampling Bias- When not all members of the population are likely to be chosen. (i.e, you only ask your friends and family about a study to do with Salinas)

  • Problems with samples: A sample must be representative of the population. A sample that is not representative of the population is biased. Biased samples that are not representative of the population give results that are inaccurate and not valid.

  • Self-selected samples: Responses only by people who choose to respond, such as call-in surveys, are often unreliable.

  • Sample size issues: Samples that are too small may be unreliable. Larger samples are better, if possible. In some situations, having small samples is unavoidable and can still be used to draw conclusions. Examples: crash testing cars or medical testing for rare conditions

  • Undue influence:  collecting data or asking questions in a way that influences the response

  • Non-response or refusal of subject to participate:  The collected responses may no longer be representative of the population.  Often, people with strong positive or negative opinions may answer surveys, which can affect the results.

  • Causality: A relationship between two variables does not mean that one causes the other to occur. They may be related (correlated) because of their relationship through a different variable.

  • Self-funded or self-interest studies: A study performed by a person or organization in order to support their claim. Is the study impartial? Read the study carefully to evaluate the work. Do not automatically assume that the study is good, but do not automatically assume the study is bad either. Evaluate it on its merits and the work done.

  • Misleading use of data: improperly displayed graphs, incomplete data, or lack of context

  • Confounding:  When the effects of multiple factors on a response cannot be separated.  Confounding makes it difficult or impossible to draw valid conclusions about the effect of each factor.

Pitanje 5
5.

Determine whether or not the following samples are representative. If they are not, write the reasons.

1. To find the average GPA of all students in a university, use all honor students at the university as the sample.

2. To find out the most popular cereal among young people under the age of ten, stand outside a large supermarket for three hours and speak to every twentieth child under age ten who enters the supermarket.

3. To find the average annual income of all adults in the United States, sample U.S. Representatives. Create a cluster sample by considering each state as a stratum (group). By using simple random sampling, select states to be part of the cluster. Then survey every U.S. Representative in the cluster.

4. To determine the proportion of people taking public transportation to work, survey 20 people in New York City. Conduct the survey by sitting in Central Park on a bench and interviewing every person who sits next to you.

5. To determine the average cost of a two-day stay in a hospital in Massachusetts, survey 100 hospitals across the state using simple random sampling.

Pitanje 6
6.

Determine what is the type of sampling in each case

  1. A sample of 100 undergraduate San Jose State students is taken by organizing the students’ names by classification (first-year, sophomore, junior, or senior), and then selecting 25 students from each.

  2. A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process.

  3. An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample.

  4. A pollster interviews all human resource personnel in five different high tech companies.

  5. A medical researcher interviews every third cancer patient from a list of cancer patients at a local hospital.

  6. A student interviews classmates in their algebra class to determine how many pairs of jeans a student owns, on the average.