Midterm Review

from datascience import *
from cs104 import *
import numpy as np
%matplotlib inline

Small Items

• You will not need to use the interact function or think about interactive visualizations on the exam.

Loops

An Example of a loop that iterates over the values of an array

# stay_positive(make_array(1,-1,-2,3,4,0)) function should return 3 -> number of positive numbers in an array.
extra_values = make_array(-1,2,3)

def stay_positive(values):
    numbers_positive = 0   # keep a count of how my positive numbers we've seen so far
    
    for value in values:
        # if my value is positive, increase number of positive numbers
        if value > 0: 
            numbers_positive = numbers_positive + 1
            
    return numbers_positive
            

stay_positive(make_array(1,-1,-2,3,4,0))

3

An Example to builds an array and returns it

def track_positives(values):
    positive_values = make_array()
    for value in values:
        # if my value is positive, increase number of positive numbers
        if value > 0: 
            positive_values = np.append(positive_values, value)
    return positive_values

track_positives(make_array(1,-1,-2,3,4,0))

array([1., 3., 4.])

An Example of a loop that iterates for a specific number of times.

def run_trials(trials):
    for i in np.arange(0,trials):
        print(2*i)

n_trials = 10     # how many trials to run
run_trials(n_trials)

0
2
4
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18

Group and Pivot

penguins = Table().read_table('data/penguins.csv')
penguins.sample(5)

species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex
Gentoo	Biscoe	46.2	14.4	214	4650	UNKNOWN
Adelie	Biscoe	39.7	18.9	184	3550	MALE
Gentoo	Biscoe	47.2	13.7	214	4925	FEMALE
Gentoo	Biscoe	47.4	14.6	212	4725	FEMALE
Adelie	Biscoe	39.6	20.7	191	3900	FEMALE

group divides the rows into groups according to the values stored in a categorical variable.

penguins.group('species')

species	count
Adelie	151
Chinstrap	68
Gentoo	123

With only one parameter, we get a count of how many rows are in each group. Pass in a second parameter that is an aggregation function to summarize the numerical columns in the table.

penguins.group('species', np.mean)

species	island mean	bill_length_mm mean	bill_depth_mm mean	flipper_length_mm mean	body_mass_g mean	sex mean
Adelie		38.7914	18.3464	189.954	3700.66
Chinstrap		48.8338	18.4206	195.824	3733.09
Gentoo		47.5049	14.9821	217.187	5076.02

We can also group by more than one column by passing in an array of the columns to group by.

penguins.group(make_array('species', 'island'), max)

species	island	bill_length_mm max	bill_depth_mm max	flipper_length_mm max	body_mass_g max	sex max
Adelie	Biscoe	45.6	21.1	203	4775	MALE
Adelie	Dream	44.1	21.2	208	4650	UNKNOWN
Adelie	Torgersen	46	21.5	210	4700	UNKNOWN
Chinstrap	Dream	58	20.8	212	4800	MALE
Gentoo	Biscoe	59.6	17.3	231	6300	UNKNOWN

pivot creates a 2-dimensional matrix by grouping according to two columns. If only those columns are provided, we get counts of how many rows fall into each row/col combination.

penguins.pivot('species', 'island')

island	Adelie	Chinstrap	Gentoo
Biscoe	44	0	123
Dream	56	68	0
Torgersen	51	0	0

Or you can pass a third column and a way to summarize that column’s values for each group:

penguins.pivot('species', 'island', 'bill_length_mm', max)

island	Adelie	Chinstrap	Gentoo
Biscoe	45.6	0	59.6
Dream	44.1	58	0
Torgersen	46	0	0

We use pivot instead of group to present data in a more accessible way, or to prepare for additional data manipulation or analyses.

Functions

Check out our lecture slides on Functions for a more complete discussion of how function definitions work, but here’s an example showing the major parts:

1. All functions start with def, the number of the function, and then the list of parameter names.

2. The body of the function is indented and contains the instructions to run when the function is called.

3. The return statement is used to give a value back to the caller.

def count_odd_values(values):
    num_odd_values = 0
    for value in values:
        if value % 2 != 0:
            num_odd_values = num_odd_values + 1
    return num_odd_values

count_odd_values(extra_values)

2

Histograms

Histograms show the distribution of values taken on by a variable. They often convey more information than just looking at the min, max, and mean. The area of each bar is proportional to the percent of data values falling with them. That percentage is computed for a bar by multiplying the width of the bar by its height.

penguins.hist('bill_length_mm')

We can adjust the bins to make the plot easier to interpret. One way is to give an array of values that will be used as the cutoffs between the bins:

cutoffs = np.arange(30,65,5)
cutoffs

array([30, 35, 40, 45, 50, 55, 60])

penguins.hist('bill_length_mm', bins=cutoffs)

We can also make an overlaid histogram:

penguins.hist('bill_length_mm', bins=cutoffs, group='species')