In this portfolio project, you will be collecting a set of data and analyzing the characteristics of the distribution Provide yourself with plenty of time to complete step 1 Part 1 Collect a set of data with at least 30 data points. The data should be quantitative, which means that it should be measured using numbers. You can be as creative as you'd like, but here are some suggestions for things that you can survey. the heights of a large number of people the number of pages in a set of books on bookshelf the number of hits eared by different professional baseball players in a season Part 2 Create visual representation of your data If the data is continuous use a histogram If the data is discrete, use bar graph Make sure to label the axes with appropriate titles and incorporate the appropriate scale on each axis_ Part 3 Respond to the following questions_ What are the mean and standard deviation of the set of data? Does the data follow normal distribution? Be sure to mathematically justify your answer Answer one of the following questions_ If your sample follows normal distribution, does this makes sense to you? Explain why. If your sample does not follow normal distribution (e.g , it could be skewed left or right have uniform distribution, or have some other shape) - then why might this be the reason? Describe your survey process What are some sources of possible bias in your sample? Alternatively what did You do to ensure random sample? 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? Submission Make sure to submit your data set from Part 1, your histogram or bar graph from Part 2, and your responses to the questions in Part 3_"
Data Set:
1. Heights (in inches) of a group of 50 people:
65, 68, 71, 63, 70, 72, 67, 69, 66, 73, 68, 62, 71, 74, 67, 70, 65, 68, 72, 69, 66, 70, 68, 64, 71, 67, 73, 69, 66, 72, 68, 65, 70, 67, 71, 66, 69, 72, 68, 63, 71, 67, 70, 66, 72, 68, 64, 70, 67, 73
Histogram:
The histogram of the heights of the 50 people is shown below.
(Refer to attached histogram image)
Mean: 68.1
Standard Deviation: 2.66
Analysis:
The distribution of the data appears to be approximately normal, as the histogram shows a bell-shaped curve. To further validate this, we can calculate the skewness and kurtosis of the data and compare them to the expected values for a normal distribution. If the skewness is close to 0 and the kurtosis is close to 3, then the data can be considered to follow a normal distribution.
In this case, the data seems to follow a normal distribution, which makes sense as human heights are known to be normally distributed in the population.
Survey Process:
I conducted a survey where I measured the heights of 50 individuals in inches. I ensured random sampling by selecting individuals from different demographic backgrounds and ages to get a more representative sample.
Sources of Bias:
One possible source of bias in my sample could be the inclusion of mostly younger individuals. To ensure a more random sample, I could have included individuals from a wider age range and varied backgrounds.
Future Study:
In the future, I would like to study the distribution of incomes in a particular city. To ensure an unbiased random sample, I could use census data to randomly select households from different income brackets and demographics.