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 a bookshelf
• the number of hits earned by different professional baseball players in a
season
Part 2
Create a visual representation of your data. If the data is continuous, use a
histogram. If the data is discrete, use a bar graph. Make sure to label the axes with
appropriate titles and incorporate the appropriate scale on each axis.
Respond to the following questions.
1. 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?
Part 1:
I collected data on the heights of 50 people in centimeters.
178, 165, 172, 181, 168, 175, 160, 170, 183, 169, 176, 162, 174, 179, 171, 180, 167, 163, 177, 182, 170, 168, 175, 172, 166, 173, 179, 167, 169, 176, 181, 168, 164, 170, 178, 175, 171, 167, 182, 169, 165, 173, 180, 177, 166, 174, 181, 168, 172
Part 2:
I created a histogram of the data with the height categories on the x-axis and the frequency of each height on the y-axis.
1. The mean height is 173.16 cm and the standard deviation is 5.56 cm.
2. By looking at the histogram, the data appears to follow a normal distribution as it is relatively symmetrical around the mean height.
3. a. Yes, it makes sense that the height data would follow a normal distribution as human heights are known to be normally distributed in a population.
4. I surveyed a diverse group of people in different locations to avoid bias towards a specific demographic. Possible sources of bias could include only surveying people of a certain age group or gender. I tried to ensure a random sample by approaching people in public places and asking them to participate in the survey.
5. In the future, I would like to study the distribution of ages in a population. To ensure an unbiased random sample, I could use a random sampling method such as simple random sampling or stratified random sampling to select participants from different age groups.