What are the mean and standard deviation of the set of data?
2. Does the data follow a normal distribution? Be sure to mathematically justify
your answer.
3. Answer one of the following questions.
a. If your sample follows a normal distribution, does this makes sense to
you? Explain why.
b. If your sample does not follow a normal distribution (e.g., it could be
skewed left or right, have a uniform distribution, or have some other
shape), then why might this be the reason?
4. Describe your survey process. What are some sources of possible bias in
your sample? Alternatively, what did you do to ensure a random sample?
5. What is a set of data that you would like to study in the future? How could
you go about ensuring an unbiased random sample?
Without a specific set of data provided, I am unable to calculate the mean and standard deviation or determine if the data follows a normal distribution. However, I can provide general information on how to address the questions presented.
To determine if a set of data follows a normal distribution, one can use statistical tests such as the Kolmogorov-Smirnov test, the Shapiro-Wilk test, or visually inspect a histogram or a Q-Q plot. If the data passes these tests or visually appears to be normally distributed, then it may make sense for the data to follow a normal distribution.
If the data does not follow a normal distribution, this could be due to a variety of reasons such as the presence of outliers, skewness, or a different underlying distribution of the data. In this case, further investigation into the data and potentially transforming the data may be necessary.
To ensure a random sample in a survey process, one can use random sampling techniques such as simple random sampling, stratified sampling, or cluster sampling. Sources of bias in a sample could include non-response bias, sampling bias, or measurement bias. To mitigate these biases, researchers can use techniques such as random sampling, ensuring a high response rate, and carefully designing the survey instrument.
In the future, a set of data I would like to study is the impact of a new educational program on student performance. To ensure an unbiased random sample, I would randomly select schools or classrooms to participate in the program and carefully monitor the implementation process to ensure consistency. I would also use pre- and post-assessments to measure student performance and account for any potential confounding variables.