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Walkthrough

Walkthrough#

Introduction#

An emerging area of biomedical research over the past decade as been the human microbiome. This field studies the commensal bacteria that inhabit our bodies and how they influence our health. These can be found everywhere from our digestive system, to our skin, to our ears, and to every part of our body. Often times hundreds of different bacterial species can be isolated from a single body site of a single individual. Disease can be caused or exacerbated by an imbalance in these species.

This week, we will explore the data generated by researchers here at Drexel. From a collection of 12 patients they measured the microbiome of of 12 body sites of the inner ear. Some of these patients had inner ear infections (otitis media) and different disease outcomes. This week, we will use Python to generate pivot-tables and bar-plots to understand whether the microbiome is impacted by disease outcome.

Learning Objectives#

At the end of this learning activity you will be able to:

  • Practice using query to extract data from a larger table.

  • Calculate summary values across a a pd.DataFrame using methods like sum, mean, and max.

  • Utilize pd.DataFrame.groupby to aggregate and transform data by group.

  • Use pd.merge to combine data held in two different tables.

  • Employ pd.pivot_table and pd.melt to reshape and summarize data.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

data = pd.read_csv('microbiome_phylum_data.tsv', sep = '\t')
data
Patient Location CollectionType Actinobacteria Bacteroidetes Firmicutes Proteobacteria num_otu Predominant
0 3062 Nasal Vestibule Swab 2516 44 14987 0 16 Firmicutes
1 3094 Nasal Vestibule Swab 103 0 1397 0 15 Firmicutes
2 3095 Nasal Vestibule Swab 1474 0 5510 29 21 Firmicutes
3 3115 Nasal Vestibule Swab 0 0 5480 0 2 Firmicutes
4 3116 Nasal Vestibule Swab 2 0 2324 1 4 Firmicutes
... ... ... ... ... ... ... ... ... ...
103 3094 Sphenoid Tissue Biopsy 1540 0 784 13 14 Actinobacteria
104 3095 Sphenoid Tissue Biopsy 670 0 703 0 14 Firmicutes
105 3116 Sphenoid Tissue Biopsy 309 9 6709 495 17 Firmicutes
106 3117 Sphenoid Tissue Biopsy 1812 0 1954 129 18 Firmicutes
107 3119 Sphenoid Tissue Biopsy 4183 0 988 13 23 Actinobacteria

108 rows × 9 columns

Exploring a single patient#

First, we’ll explore the distribution of bacteria of a single individual across body site.

Q1: Extract the information for patient 3116#

pat_3116 = data.query('Patient == 3116')  # SOLUTION

pat_3116.head()
Patient Location CollectionType Actinobacteria Bacteroidetes Firmicutes Proteobacteria num_otu Predominant
4 3116 Nasal Vestibule Swab 2 0 2324 1 4 Firmicutes
14 3116 Head of Inferior Turbinate Tissue Biopsy 19 0 6261 21 5 Firmicutes
25 3116 Middle Meatus Swab 5 0 988 2 10 Firmicutes
36 3116 Uncinate Process Tissue Biopsy 17 0 7249 79 12 Firmicutes
42 3116 Maxillary Sinus Swab 34 0 5748 190 11 Firmicutes 
print(f'pat_3116 is an `DataFrame`: {isinstance(pat_3116, pd.DataFrame)}')

pat_3116 is an `DataFrame`: True

print(f'len(pat_3116) = {len(pat_3116)}')

len(pat_3116) = 12

# Checking for specific rows.
print(f'pat_3116["Actinobacteria"].sum() = {pat_3116["Actinobacteria"].sum()}')

pat_3116["Actinobacteria"].sum() = 1145

Q2: Calculate the average count across regions for each phylum for patient 3116.#

q2_Actinobacteria_mean = pat_3116['Actinobacteria'].mean() # SOLUTION
q2_Bacteroidetes_mean = pat_3116['Bacteroidetes'].mean() # SOLUTION
q2_Firmicutes_mean = pat_3116['Firmicutes'].mean() # SOLUTION
q2_Proteobacteria_mean = pat_3116['Proteobacteria'].mean() # SOLUTION

print(f'q2_Actinobacteria_mean = {q2_Actinobacteria_mean:0.2f}')

q2_Actinobacteria_mean = 95.42

print(f'q2_Bacteroidetes_mean = {q2_Bacteroidetes_mean:0.2f}')

q2_Bacteroidetes_mean = 1.25

print(f'q2_Firmicutes_mean = {q2_Firmicutes_mean:0.2f}')

q2_Firmicutes_mean = 5135.50

print(f'q2_Proteobacteria_mean = {q2_Proteobacteria_mean:0.2f}')

q2_Proteobacteria_mean = 299.75

Summarizing by grouping#

Now that we’ve looked at the summary values for a single individual, how would we look at this for each individual? Copy-pasting that over and over is unsustainable, DataFrames have useful methods for dealing with this problem.

All of these fall into the same basic strategy.

Split - Apply - Combine.

# Split

grouped_patients = data.groupby('Patient')

# Apply - Combine

# Capitalizing constants is useful if you will re-use them often.
PHYLUM_COLS = ['Actinobacteria', 'Bacteroidetes',
                'Firmicutes', 'Proteobacteria']

mean_vals = grouped_patients[PHYLUM_COLS].mean()
mean_vals
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
Patient
3062 727.571429 7.714286 4513.714286 2.000000
3094 1356.900000 0.100000 2384.300000 79.100000
3095 1447.111111 0.111111 2753.666667 47.777778
3115 49.875000 1.375000 4266.875000 22.000000
3116 95.416667 1.250000 5135.500000 299.750000
3117 1164.333333 0.000000 1859.777778 69.000000
3118 1329.125000 3.125000 3271.125000 224.375000
3119 2692.727273 0.000000 1437.636364 5.727273
3120 1679.333333 0.000000 1435.555556 18.888889
3121 1205.428571 18.571429 3486.142857 29.714286
3123 1852.142857 12.285714 2536.428571 129.285714
3124 1603.545455 0.000000 1998.545455 39.272727 
# This is commonly done in a single "sentence"

mean_vals = data.groupby('Patient')[PHYLUM_COLS].mean()

Q3: Calculate the average counts of each phylum by body site.#

q3_mean_phylum_site = data.groupby('Location')[PHYLUM_COLS].mean() # SOLUTION

q3_mean_phylum_site
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
Location
Ethmoid Culture (Deep to Ethmoid Bulla) 1483.750000 3.416667 2757.416667 127.000000
Ethmoid Tissue (Deep to Ethmoid Bulla) 1449.444444 0.777778 1715.555556 92.111111
Head of Inferior Turbinate Tissue 317.000000 0.636364 2165.727273 24.727273
Maxillary Sinus 1691.000000 0.000000 3002.750000 122.500000
Maxillary Sinus Tissue 976.666667 0.000000 2966.000000 77.000000
Middle Meatus 1158.363636 0.181818 3131.363636 43.000000
Nasal Vestibule 1161.400000 12.500000 4373.000000 37.900000
Sphenoethmoidal Recess Tissue 930.888889 4.000000 2019.666667 175.777778
Sphenoid 1974.750000 5.416667 3821.000000 69.666667
Sphenoid Tissue 1702.800000 1.800000 2227.600000 130.000000
Superior Meatus 1704.416667 1.166667 3547.250000 127.416667
Uncinate Process Tissue 868.900000 1.700000 2259.600000 40.700000 
print(f'q3_mean_phylum_site is a `DataFrame`: {isinstance(q3_mean_phylum_site, pd.DataFrame)}')

q3_mean_phylum_site is a `DataFrame`: True

print(f'q3_mean_phylum_site.index = {list(q3_mean_phylum_site.index)}')

q3_mean_phylum_site.index = ['Ethmoid Culture (Deep to Ethmoid Bulla)', 'Ethmoid Tissue (Deep to Ethmoid Bulla)', 'Head of Inferior Turbinate Tissue', 'Maxillary Sinus', 'Maxillary Sinus Tissue', 'Middle Meatus', 'Nasal Vestibule', 'Sphenoethmoidal Recess Tissue', 'Sphenoid', 'Sphenoid Tissue', 'Superior Meatus', 'Uncinate Process Tissue']

print(f'q3_mean_phylum_site.columns = {list(q3_mean_phylum_site.columns)}')

q3_mean_phylum_site.columns = ['Actinobacteria', 'Bacteroidetes', 'Firmicutes', 'Proteobacteria']

print(f'q3_mean_phylum_site.sum().sum() = {q3_mean_phylum_site.sum().sum():0.2f}')

q3_mean_phylum_site.sum().sum() = 50505.71

There are a number of different built-in summary functions like this.

data.groupby('Patient')[PHYLUM_COLS].median()
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
Patient
3062 461.0 2.0 2714.0 0.0
3094 1000.0 0.0 1467.5 41.5
3095 1223.0 0.0 1244.0 15.0
3115 15.0 0.0 2846.5 1.5
3116 37.0 0.0 6004.5 183.5
3117 1108.0 0.0 1800.0 66.0
3118 1023.5 0.0 3343.0 152.5
3119 2605.0 0.0 988.0 3.0
3120 468.0 0.0 1301.0 27.0
3121 911.0 12.0 3686.0 13.0
3123 1010.0 0.0 1207.0 63.0
3124 1602.0 0.0 2133.0 19.0 
data.groupby('Patient')[PHYLUM_COLS].count()
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
Patient
3062 7 7 7 7
3094 10 10 10 10
3095 9 9 9 9
3115 8 8 8 8
3116 12 12 12 12
3117 9 9 9 9
3118 8 8 8 8
3119 11 11 11 11
3120 9 9 9 9
3121 7 7 7 7
3123 7 7 7 7
3124 11 11 11 11 
data.groupby('Patient')[PHYLUM_COLS].max()
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
Patient
3062 2516 44 14987 6
3094 4604 1 5559 406
3095 3926 1 10097 166
3115 211 11 13948 108
3116 340 9 9796 1139
3117 1812 0 3671 129
3118 3709 12 5253 771
3119 7514 0 4372 18
3120 4195 0 2655 36
3121 2816 63 6135 78
3123 4186 81 5885 323
3124 4138 0 3979 183

You can see an extensive list of available summary functions at the Pandas Documentation

If there isn’t a function that does what you want, you can also make your own.

Here is a simple one that scales the data to a unit-norm.

def unit_norm(values):
    "Given a series, return a scaled version"

    mu = values.mean()
    std = values.std()

    return (values-mu)/std

unit_normed_data = data.groupby('Patient', as_index=False)[PHYLUM_COLS].transform(unit_norm)

unit_normed_data
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
0 2.158109 2.247876 2.140374 -0.755929
1 -0.901854 -0.316228 -0.515722 -0.660942
2 0.025250 -0.333333 0.862714 -0.303077
3 -0.694809 -0.353553 0.287822 -0.549657
4 -0.790041 -0.441315 -0.985677 -0.838082
... ... ... ... ...
103 0.131693 -0.316228 -0.835926 -0.552316
104 -0.729756 -0.333333 -0.641845 -0.771142
105 1.806312 2.736155 0.551650 0.547734
106 1.315743 NaN 0.101533 1.390656
107 0.700800 NaN -0.331381 1.106277

108 rows × 4 columns

Notice I used the transform method here instead of a common name.

When applying custom functions to groups of data there are three different methods depending on your final output shape:

  • .aggregate() or .agg() - Each group of data produces a single summary number. Commonly used to summarize groups.

  • .transform() - The output will have the same number (and order) of rows as the input. Commonly used for normalizations.

  • .apply() - Everything else.

Merging data#

Now we come to a common problem, our sample information is in a different file.

sample_info = pd.read_csv('sample_info.csv')
sample_info.head()
PID severe_disease disease_type
0 3062 False persistent
1 3094 False persistent
2 3095 False persistent
3 3115 True typical
4 3116 True typical

Now that we have two DataFrames with a common key we can use pd.merge.

merged_info = pd.merge(data, sample_info,
                       left_on = 'Patient', # The column of the key in biome_data
                       right_on = 'PID', # The column of the key in sample_info
                       how = 'inner') # Keep only those in both

merged_info.head()
Patient Location CollectionType Actinobacteria Bacteroidetes Firmicutes Proteobacteria num_otu Predominant PID severe_disease disease_type
0 3062 Nasal Vestibule Swab 2516 44 14987 0 16 Firmicutes 3062 False persistent
1 3094 Nasal Vestibule Swab 103 0 1397 0 15 Firmicutes 3094 False persistent
2 3095 Nasal Vestibule Swab 1474 0 5510 29 21 Firmicutes 3095 False persistent
3 3115 Nasal Vestibule Swab 0 0 5480 0 2 Firmicutes 3115 True typical
4 3116 Nasal Vestibule Swab 2 0 2324 1 4 Firmicutes 3116 True typical

Q4: Calculate the average counts of each phylum by severe_disease.#

q4_severe_means = merged_info.groupby('severe_disease')[PHYLUM_COLS].mean() # SOLUTION

print(f'q4_severe_means is a `DataFrame`: {isinstance(q4_severe_means, pd.DataFrame)}')

q4_severe_means is a `DataFrame`: True

print(f'q4_severe_means.index = {list(q4_severe_means.index)}')

q4_severe_means.index = [False, True]

print(f'q4_severe_means.columns = {list(q4_severe_means.columns)}')

q4_severe_means.columns = ['Actinobacteria', 'Bacteroidetes', 'Firmicutes', 'Proteobacteria']

print(f'q4_severe_means.sum().sum() = {q4_severe_means.sum().sum():0.2f}')

q4_severe_means.sum().sum() = 8544.57

We can also do more advanced things like this:

merged_info.groupby(['Location', 'severe_disease'])[PHYLUM_COLS].aggregate(['mean', 'std'])
Actinobacteria Bacteroidetes Firmicutes Proteobacteria
mean std mean std mean std mean std
Location severe_disease
Ethmoid Culture (Deep to Ethmoid Bulla) False 1382.714286 875.245435 4.142857 10.106575 2053.142857 1314.670989 31.571429 32.444091
True 1625.200000 1698.904706 2.400000 5.366563 3743.400000 3394.971988 260.600000 492.952127
Ethmoid Tissue (Deep to Ethmoid Bulla) False 1689.400000 1065.430570 0.000000 0.000000 1232.200000 722.258403 91.400000 64.103822
True 1149.500000 1066.299676 1.750000 3.500000 2319.750000 2767.632728 93.000000 125.078642
Head of Inferior Turbinate Tissue False 394.833333 282.110912 1.166667 2.401388 1123.333333 343.322395 19.500000 26.883080
True 223.600000 219.127360 0.000000 0.000000 3416.600000 2021.523510 31.000000 42.023803
Maxillary Sinus False 2539.500000 2260.620379 0.000000 0.000000 2999.000000 1224.708945 150.000000 193.747258
True 842.500000 1143.391665 0.000000 0.000000 3006.500000 3877.066481 95.000000 134.350288
Maxillary Sinus Tissue False 265.000000 NaN 0.000000 NaN 448.000000 NaN 17.000000 NaN
True 1332.500000 1827.871029 0.000000 0.000000 4225.000000 5392.396313 107.000000 147.078210
Middle Meatus False 1171.000000 747.548527 0.333333 0.816497 2916.166667 940.973627 19.666667 18.062853
True 1143.200000 1343.776097 0.000000 0.000000 3389.600000 1624.755459 71.000000 97.739450
Nasal Vestibule False 1598.000000 1496.139811 17.857143 32.313199 4987.000000 4857.272383 52.714286 119.600326
True 142.666667 245.375902 0.000000 0.000000 2940.333333 2294.448154 3.333333 4.932883
Sphenoethmoidal Recess Tissue False 1286.000000 1863.761385 6.200000 11.278298 1723.600000 2203.662020 95.000000 174.608133
True 487.000000 427.834080 1.250000 2.500000 2389.750000 1640.061660 276.750000 382.792698
Sphenoid False 1953.428571 1362.865958 9.142857 23.751692 3441.000000 2253.827337 35.142857 36.503098
True 2004.600000 3145.778966 0.200000 0.447214 4353.000000 5425.135298 118.000000 124.715677
Sphenoid Tissue False 1105.000000 615.182900 0.000000 0.000000 743.500000 57.275649 6.500000 9.192388
True 2101.333333 1953.139609 3.000000 5.196152 3217.000000 3062.488694 212.333333 251.573714
Superior Meatus False 2235.000000 1402.061102 2.000000 4.472136 4252.285714 2796.542014 75.000000 69.622793
True 961.600000 847.056846 0.000000 0.000000 2560.200000 1857.766186 200.800000 326.720370
Uncinate Process Tissue False 766.400000 718.500383 0.000000 0.000000 1440.200000 291.232210 18.400000 17.700282
True 971.400000 1580.324745 3.400000 4.979960 3079.000000 2892.901658 63.000000 60.930288

Here I’ve broken things down by body-site and disease status and calculated both a mean and standard deviation. In future lectures we will explore how to quantify this with a significance test. For now, we’ll leave it as a visual comparison.

Pivoting & Melting Dataframes#

This is a process of reshaping, and optionally summarizing, your data as you convert it between wide and long format. These techniques are often required for generating different types of plots.

These are best shown by example.

Pivoting#

long -> wide

pd.pivot_table(merged_info,
               index = 'Patient',
               columns = 'Location',
               values = 'Firmicutes',
               aggfunc = 'mean')
Location Ethmoid Culture (Deep to Ethmoid Bulla) Ethmoid Tissue (Deep to Ethmoid Bulla) Head of Inferior Turbinate Tissue Maxillary Sinus Maxillary Sinus Tissue Middle Meatus Nasal Vestibule Sphenoethmoidal Recess Tissue Sphenoid Sphenoid Tissue Superior Meatus Uncinate Process Tissue
Patient
3062 2714.0 NaN 1746.0 NaN NaN 1822.0 14987.0 NaN 6125.0 NaN 2992.0 1210.0
3094 385.0 664.0 1089.0 NaN NaN 4316.0 1397.0 5559.0 4648.0 784.0 3463.0 1538.0
3095 2300.0 651.0 760.0 NaN NaN 2999.0 5510.0 NaN 519.0 703.0 10097.0 1244.0
3115 2168.0 NaN 4640.0 NaN NaN 3525.0 5480.0 1861.0 13948.0 NaN 982.0 1531.0
3116 9796.0 6357.0 6261.0 5748.0 8038.0 988.0 2324.0 3673.0 617.0 6709.0 3866.0 7249.0
3117 1800.0 672.0 1499.0 NaN NaN 2810.0 1017.0 NaN 2082.0 1954.0 3671.0 1233.0
3118 2459.0 380.0 2962.0 NaN NaN 5253.0 NaN 3724.0 2322.0 NaN 4144.0 4925.0
3119 2494.0 1870.0 1721.0 265.0 412.0 4372.0 NaN 301.0 2796.0 988.0 138.0 457.0
3120 905.0 1614.0 1136.0 NaN NaN 2342.0 515.0 415.0 2655.0 NaN 2037.0 1301.0
3121 3060.0 NaN 863.0 NaN NaN 3686.0 4295.0 1624.0 6135.0 NaN 4740.0 NaN
3123 1029.0 914.0 NaN 3865.0 NaN NaN 5885.0 358.0 1207.0 NaN 4497.0 NaN
3124 3979.0 2318.0 1146.0 2133.0 448.0 2332.0 2320.0 662.0 2798.0 NaN 1940.0 1908.0

This took our “long” data format in which each row represented the observation at a different site of a different person and converted it into a “wide” data format such that each row is a patient and each column is a number of Firmicutes at a location. NaNs represent missing information.

We also had to “give up” some information for this transformation … this is only Firmicutes.

One can do this to include more information:

pd.pivot_table(merged_info,
               index = 'Patient',
               columns = 'Location',
               values = ['Actinobacteria', 'Firmicutes'],
               aggfunc = 'mean')
Actinobacteria ... Firmicutes
Location Ethmoid Culture (Deep to Ethmoid Bulla) Ethmoid Tissue (Deep to Ethmoid Bulla) Head of Inferior Turbinate Tissue Maxillary Sinus Maxillary Sinus Tissue Middle Meatus Nasal Vestibule Sphenoethmoidal Recess Tissue Sphenoid Sphenoid Tissue ... Head of Inferior Turbinate Tissue Maxillary Sinus Maxillary Sinus Tissue Middle Meatus Nasal Vestibule Sphenoethmoidal Recess Tissue Sphenoid Sphenoid Tissue Superior Meatus Uncinate Process Tissue
Patient
3062 461.0 NaN 232.0 NaN NaN 292.0 2516.0 NaN 623.0 NaN ... 1746.0 NaN NaN 1822.0 14987.0 NaN 6125.0 NaN 2992.0 1210.0
3094 243.0 638.0 282.0 NaN NaN 1486.0 103.0 4604.0 2690.0 1540.0 ... 1089.0 NaN NaN 4316.0 1397.0 5559.0 4648.0 784.0 3463.0 1538.0
3095 1652.0 1038.0 444.0 NaN NaN 2010.0 1474.0 NaN 587.0 670.0 ... 760.0 NaN NaN 2999.0 5510.0 NaN 519.0 703.0 10097.0 1244.0
3115 80.0 NaN 1.0 NaN NaN 13.0 0.0 211.0 17.0 NaN ... 4640.0 NaN NaN 3525.0 5480.0 1861.0 13948.0 NaN 982.0 1531.0
3116 340.0 61.0 19.0 34.0 40.0 5.0 2.0 181.0 32.0 309.0 ... 6261.0 5748.0 8038.0 988.0 2324.0 3673.0 617.0 6709.0 3866.0 7249.0
3117 1546.0 1108.0 521.0 NaN NaN 965.0 426.0 NaN 1537.0 1812.0 ... 1499.0 NaN NaN 2810.0 1017.0 NaN 2082.0 1954.0 3671.0 1233.0
3118 1802.0 824.0 332.0 NaN NaN 1465.0 NaN 454.0 923.0 NaN ... 2962.0 NaN NaN 5253.0 NaN 3724.0 2322.0 NaN 4144.0 4925.0
3119 4358.0 2605.0 245.0 1651.0 2625.0 3268.0 NaN 1102.0 7514.0 4183.0 ... 1721.0 265.0 412.0 4372.0 NaN 301.0 2796.0 988.0 138.0 457.0
3120 2740.0 3265.0 68.0 NaN NaN 405.0 107.0 468.0 4195.0 NaN ... 1136.0 NaN NaN 2342.0 515.0 415.0 2655.0 NaN 2037.0 1301.0
3121 1971.0 NaN 452.0 NaN NaN 911.0 582.0 399.0 2816.0 NaN ... 863.0 NaN NaN 3686.0 4295.0 1624.0 6135.0 NaN 4740.0 NaN
3123 1010.0 2263.0 NaN 941.0 NaN NaN 4186.0 226.0 861.0 NaN ... NaN 3865.0 NaN NaN 5885.0 358.0 1207.0 NaN 4497.0 NaN
3124 1602.0 1243.0 891.0 4138.0 265.0 1922.0 2218.0 733.0 1902.0 NaN ... 1146.0 2133.0 448.0 2332.0 2320.0 662.0 2798.0 NaN 1940.0 1908.0

12 rows × 24 columns

But that is usually not a great idea.

Melting#

wide -> long

Our data is part long and part wide (like most real datasets). In some plotting instances we may want to make it “longer” by having each bacteria be a diffent row instead of a different column.

pd.melt(merged_info,
        id_vars = ['Patient', 'Location'], # The things you want preserved in each row
        value_vars = PHYLUM_COLS, # The columns you want to melt
        var_name = 'Phylum', # The name of the column that will have the value_var name
        value_name = 'Counts') # The name of the column that will have the value
Patient Location Phylum Counts
0 3062 Nasal Vestibule Actinobacteria 2516
1 3094 Nasal Vestibule Actinobacteria 103
2 3095 Nasal Vestibule Actinobacteria 1474
3 3115 Nasal Vestibule Actinobacteria 0
4 3116 Nasal Vestibule Actinobacteria 2
... ... ... ... ...
427 3094 Sphenoid Tissue Proteobacteria 13
428 3095 Sphenoid Tissue Proteobacteria 0
429 3116 Sphenoid Tissue Proteobacteria 495
430 3117 Sphenoid Tissue Proteobacteria 129
431 3119 Sphenoid Tissue Proteobacteria 13

432 rows × 4 columns

We’ll explore these in more detail as we move into plotting next week. This is just a taste.

Submission#

Submit this assignment through BBLearn.

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