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Stats with SciPy

For this problem set, we will be using real data. We will analyze the height and weight of the athletes at the 2012 London Olympics. You can find the CSV for this dataset here.

Reading the Data

  1. Use DictReader from import csv to read the CSV data file into a list of dictionaries named athletes, where each row is a dictionary.
  2. Create a list named ages that is a simple list of integers of all the ages in our file.
  3. Create two lists named ages_female and ages_male that is a simple list of integers of the ages of female and male athletes.
  4. Create three lists weights, weights_female, and weights_male, much like parts 2 and 3, that are simple lists of integers values of the weights from athletes.
  5. Create three lists heights, heights_female, and heights_male, much like parts 2 and 3, that are simple lists of integers values of the heights from athletes.
  6. Create a list called bmi, which is a list of the body mass index (BMI) values for each athlete in our list. (HINT: BMI = weight {kg} / (height {meters} * height {meters}).)
  7. Much like part 5, create two lists bmi_female and bmi_male, which include just the BMI values for the female and male atheletes respectively.

NOTE: This problem set deals with the BMI because it is easy to calculate for this particular data set. However, the BMI has many limitations, and it does not fully represent the health of the human body.

Basic Stats

  1. Find the mean and standard deviation of: ages, ages_female, and ages_male. What do you now know about the age of Olympic athletes? Is this what you expected?
  2. Find the mean and standard deviation of: heights, heights_female, and heights_male. We probably expect the average man to be somewhat taller than the averge woman. Is that true for Olympic athletes?
  3. Find the mean and standard deviation of: weights, weights_female, and weights_male. We probably expect the average man to be somewhat heavier than the averge woman. Is that true for Olympic athletes?
  4. Find he mean and standard deviation of: bmi, bmi_female, and bmi_male. What is a typical BMI for an Olympic athlete?

Stats

  1. How do the geometric mean and harmonic mean compare for heights_female?
  2. How do the geometric mean and harmonic mean compare for weights_male?
  3. Build a 10-bin histogram from the bmi list.
  4. Build a histogram for the heights_female and heights_male lists, starting at 120 cm and going to up to 220 cm in 10 cm increments.

Percentiles

If Angelina Jolie and Brad Pitt were in the athletes list above, here is what their lines would look like:

{'Name': 'Angelina Jolie', 'Age': '40', 'Sex': 'F', 'Weight (kg)': '56.5', 'Sport': 'Acting', 'Height (cm)': '173'}
{'Name': 'Brad Pitt', 'Age': '52', 'Sex': 'M', 'Weight (kg)': '78', 'Sport': 'Acting', 'Height (cm)': '180'}
  1. What percentile is Angelina Jolie's weight, compared to the weights_female list?
  2. What percentile is Brad Pitt's height, compared to the heights_male list?
  3. What percentile would Angelina and Brad fall into in bmi_female and bmi_male respectively?
  4. What percentile would YOU fall into, in your respective sex height, weight, and bmi? (No judgements!)

Interpolation

Let's try and fit our data. First, we will try to interpolate between the age and the BMI of our Olympic athletes. As it happens, interpolation is meant for the situation where we have one X value for one Y value. Since we have many duplicate ages among our athletes, this is not a good fit. While taking a small sample of the data is fine for education, it is probably not what we would do with this data in real life.

  1. Use dict and zip to make a dictionary of the first 25 athletes in your ages and bmi lists. Name your dictionary bmi_by_age.
  2. Create a ordered list, named age_keys of the ages in bmi_by_age. (Use sorted and .keys().)
  3. Create a list, named bmi_values, of the bmi values associate with each age in age_keys. (Use a for loop and your age_keys along with bmi_by_age.)
  4. Create a function f_linear that is an interpolation of age_keys and bmi_values. (Use interp1d.)
  5. Create a function f_cubic that is a cubic interpolation of age_keys and bmi_values. (Use interp1d along with kind='cubic'.)
  6. Try different ages in your f_linear and f_cubic functions. How well do they match each other? How well do they match the data? Do they make sense?

Optimize

Let's try to analyze all of our data points (athletes) in a slightly more realistic way. A good start would be to use a more general curve-fitting approach.

Just to help you through the process, here is the data you're trying to fit:

Olympic Female Age vs BMI

  1. Convert the following from lists to numpy.array: ages_female, ages_male, bmi_female, and bmi_male.
  2. Create a function named linear that takes x, a, and b and returns ax + b.
  3. Use curve_fit and your linear function to fit the data where female athletes ages are the x-value and female athletes BMI are the y-values. Do you think your fitted function matches the plot above?
  4. Use curve_fit and your linear function to fit the data where male athletes ages are the x-value and male athletes BMI are the y-values. Do you think your fitted function seems reasonable? How could you test that?

Solutions

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