Exploring Mathematics and Data Science with Technology

(a)

Repeat the steps from previous sections to get a copy of pizza_table available for this notebook.

(b)

The table in 3.3.2 describes how many pizzas of each type (Chicken, Classic, Supreme, Veggie) were sold on June 20th.

This table was created by running june20_pizzas = pizza_table.where("date","2015-06-20").group("type") and june20_pizzas.show(). Modify this code to create the table may18 for May 18th instead, and show the result.

(c)

The bar chart in 3.3.3 visualizes the amounts of each pizza type sold on June 20. Each category (in this case, the type of pizza) is listed on the vertical axis, and the size of the bar in the horizontal direction represents each numerical value.

Create a similar bar chart by hand for the May 18th table you displayed in the previous task.

(d)

The Python datascience library can produce bar charts; the code june20_pizzas.barh("types") was used to produce 3.3.3. Adapt this line of code to generate a bar chart for the May 18th data instead. (Note: you'll need to run import matplotlib and %matplotlib inline first to display any visualizations.)

(e)

The code pizza_table.where("date","2015-06-20").select("type","price").group("type",sum) captures the total sales for each type of pizza sold on June 20th.

Generate a bar chart visualizing the total sales for each type of pizza sold on May 18th.

(a)

Right now, the date for each pizza sold is stored as a string of numbers and hyphens, such as "2015-08-19". The code in 3.3.4 provides a datetime column with values that Python understands better. (This is another example of “cleaning” data for analysis.)

# converts `date` string into a native datetime format
from datetime import datetime
pizza_table = pizza_table.with_column("datetime",pizza_table.apply(
    lambda x:datetime.strptime(x,"%Y-%m-%d"),"date"
))

Use this script to update your pizza_table. Show twenty rows of the resulting table below to confirm that it has both a date column (which stores strings) and a datetime column (which stores datetimes).

(b)

The code in 3.3.5 displays the total number of pizzas sold each day of 2015 as the line chart given in 3.3.6.

# .plot("datetime") creates a line chart with the datetime column on the
# horizontal axis, and other numerical columns on the vertical axis
pizza_table.select("datetime","price").group("datetime").plot("datetime")

Write a sentence describing the approximate time of year when the pizza parlor's best day of sales occurred, and how you determined this from the line chart.

(c)

Copy 3.3.5 into a new Code cell, but modify .group("datetime") so that instead of showing the number of pizzas sold each day, the total (sum) of sales for each day are shown in the line chart instead.

(a)

Create a table called testing_table populated with the “Math Placement Exam Results” dataset found at https://vincentarelbundock.github.io/Rdatasets/datasets.html. This dataset describes the mathematics testing results from several freshmen students at a liberal arts college, including SAT, ACT, and the college's internal math placement exam results.

Show the first ten rows of this table.

(b)

You'll see many “Not a Number” nan values in this table for when data was not available. To clean this data for analysis, you should remove these records as needed by only using values that are positive.

Use from datascience.predicates import are and .where(column_name,are.above(0)) to, show the first ten rows of this table that don't have a nan score for SAT math scores.

(c)

The script in 3.3.7 results in a scatter plot. Each dot represents a different student's SAT Math score (by its horizontal position) with their college math placement score (by its vertical position). Note that scores of nan and other non-positive results are ignored.

# The backslash can be used to continue a long line on multiple lines
testing_table.where("PlcmtScore",are.above(0)).where("SATM",are.above(0)) \
    .select("SATM","PlcmtScore").scatter("SATM")

Run a modified copy of this script in a Code cell to display a scatter plot that compares ACT Math scores with college math placement scores.

(d)

When two values of data are correlated (that is, possibly influenced by one another), this correlation is often apparent when visualized in a scatter plot.

Do you think SAT Math scores and correlated with this college's math placement exam results? What about ACT Math scores? Write a few sentences explaining why or why not.

(e)

Suppose you heard someone claim that this college's math placement score doesn't measure mathematical ability, but instead only reflects the size of each student's high school.

Show a scatter plot comparing the size of each student's high school with their math placement score. Then write a sentence or two explaining whether you agree with this claim or not, based on the scatter plot.

(f)

Suppose you heard someone claim that students shouldn't have to take a math placement test once they come to this college, and SAT or ACT socres should be used instead. Based on the scatter plots above, would you agree or disagree with that statement? Write a few sentences explaining your reasoning.