Complete all **Exercises**, and submit answers to **Questions** on the Coursera
platform.

Some define statistics as the field that focuses on turning information into knowledge. The first step in that process is to summarize and describe the raw information - the data. In this lab we explore flights, specifically a random sample of domestic flights that departed from the three major New York City airport in 2013. We will generate simple graphical and numerical summaries of data on these flights and explore delay times. As this is a large data set, along the way you'll also learn the indispensable skills of data processing and subsetting.

In this lab we will explore the data using the `dplyr`

package and visualize it
using the `ggplot2`

package for data visualization. The data can be found in the
companion package for this course, `statsr`

.

Let's load the packages.

```
In [1]:
```library(statsr)
library(dplyr)
library(ggplot2)

```
```

The Bureau of Transportation Statistics (BTS) is a statistical agency that is a part of the Research and Innovative Technology Administration (RITA). As its name implies, BTS collects and makes available transportation data, such as the flights data we will be working with in this lab.

We begin by loading the `nycflights`

data frame. Type the following in your console
to load the data:

```
In [2]:
```data(nycflights)

The data frame containing 32735 flights that shows up in your workspace is a data matrix, with each row representing an observation and each column representing a variable. R calls this data format a data frame, which is a term that will be used throughout the labs.

To view the names of the variables, type the command

```
In [3]:
```names(nycflights)

```
Out[3]:
```

```
In [4]:
```str(nycflights)

```
```

This returns the names of the variables in this data frame. The **codebook**
(description of the variables) is included below. This information can also be
found in the help file for the data frame which can be accessed by typing
`?nycflights`

in the console.

`year`

,`month`

,`day`

: Date of departure`dep_time`

,`arr_time`

: Departure and arrival times, local timezone.`dep_delay`

,`arr_delay`

: Departure and arrival delays, in minutes. Negative times represent early departures/arrivals.`carrier`

: Two letter carrier abbreviation.`9E`

: Endeavor Air Inc.`AA`

: American Airlines Inc.`AS`

: Alaska Airlines Inc.`B6`

: JetBlue Airways`DL`

: Delta Air Lines Inc.`EV`

: ExpressJet Airlines Inc.`F9`

: Frontier Airlines Inc.`FL`

: AirTran Airways Corporation`HA`

: Hawaiian Airlines Inc.`MQ`

: Envoy Air`OO`

: SkyWest Airlines Inc.`UA`

: United Air Lines Inc.`US`

: US Airways Inc.`VX`

: Virgin America`WN`

: Southwest Airlines Co.`YV`

: Mesa Airlines Inc.

`tailnum`

: Plane tail number`flight`

: Flight number`origin`

,`dest`

: Airport codes for origin and destination. (Google can help you with what code stands for which airport.)`air_time`

: Amount of time spent in the air, in minutes.`distance`

: Distance flown, in miles.`hour`

,`minute`

: Time of departure broken in to hour and minutes.

A very useful function for taking a quick peek at your data frame, and viewing
its dimensions and data types is `str`

, which stands for **str**ucture.

The nycflights data frame is a massive trove of information. Let’s think about some questions we might want to answer with these data:

We might want to find out how delayed flights headed to a particular destination tend to be. We might want to evaluate how departure delays vary over months. Or we might want to determine which of the three major NYC airports has a better on time percentage for departing flights.

The `dplyr`

package offers seven verbs (functions) for basic data
manipulation:

`filter()`

`arrange()`

`select()`

`distinct()`

`mutate()`

`summarise()`

`sample_n()`

We will use some of these functions in this lab, and learn about others in a future lab.

We can examine the distribution of departure delays of all flights with a histogram.

```
In [5]:
```ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram()

```
```

This function says to plot the dep_delay variable from the nycflights data frame on the x-axis. It also defines a geom (short for geometric object), which describes the type of plot you will produce.

Histograms are generally a very good way to see the shape of a single distribution, but that shape can change depending on how the data is split between the different bins. You can easily define the binwidth you want to use:

```
In [6]:
```ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 15)

```
```

```
In [7]:
```ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 150)

```
```

```
In [8]:
```rdu_flights <- nycflights %>%
filter(dest == "RDU")
ggplot(data = rdu_flights, aes(x = dep_delay)) +
geom_histogram()

```
```

Let's decipher these three lines of code:

- Line 1: Take the
`nycflights`

data frame,`filter`

for flights headed to RDU, and save the result as a new data frame called`rdu_flights`

.`==`

means "if it's equal to".`RDU`

is in quotation marks since it is a character string.

- Line 2: Basically the same
`ggplot`

call from earlier for making a histogram, except that it uses the data frame for flights headed to RDU instead of all flights.

Filtering for certain observations (e.g. flights from a
particular airport) is often of interest in data frames where we might want to
examine observations with certain characteristics separately from the rest of
the data. To do so we use the `filter`

function and a series of
**logical operators**. The most commonly used logical operators for data
analysis are as follows:

`==`

means "equal to"`!=`

means "not equal to"`>`

or`<`

means "greater than" or "less than"`>=`

or`<=`

means "greater than or equal to" or "less than or equal to"

We can also obtain numerical summaries for these flights:

```
In [12]:
```rdu_flights %>%
summarise(mean_dd = mean(dep_delay), sd_dd = sd(dep_delay), n = n())

```
Out[12]:
```

Note that in the `summarise`

function we created a list of two elements. The
names of these elements are user defined, like `mean_dd`

, `sd_dd`

, `n`

, and
you could customize these names as you like (just don't use spaces in your
names). Calculating these summary statistics also require that you know the
function calls. Note that `n()`

reports the sample size.

Some useful function calls for summary statistics for a single numerical variable are as follows:

`mean`

`median`

`sd`

`var`

`IQR`

`range`

`min`

`max`

</div>

We can also filter based on multiple criteria. Suppose we are interested in flights headed to San Francisco (SFO) in February:

```
In [15]:
```sfo_feb_flights <- nycflights %>%
filter(dest == "SFO", month == 2)

Note that we can separate the conditions using commas if we want flights that
are both headed to SFO **and** in February. If we are interested in either
flights headed to SFO **or** in February we can use the `|`

instead of the comma.

1.
Create a new data frame that includes flights headed to SFO in February, and save
this data frame as `sfo_feb_flights`

. How many flights meet these criteria?

- 68
- 1345
- 2286
- 3563
- 32735

```
In [17]:
```nrow(sfo_feb_flights)

```
Out[17]:
```

2.
Make a histogram and calculate appropriate summary statistics for **arrival
delays ** of `sfo_feb_flights`

. Which of the following is false?

- The distribution is unimodal.
- The distribution is right skewed.
- No flight is delayed more than 2 hours.
- The distribution has several extreme values on the right side.
- More than 50% of flights arrive on time or earlier than scheduled.

```
In [19]:
```ggplot(data = sfo_feb_flights, aes(x = arr_delay)) +
geom_histogram() # C is wrong, so choose 3

```
```

```
In [ ]:
```

`group_by`

function to get the same summary stats for
each origin airport:

```
In [20]:
```rdu_flights %>%
group_by(origin) %>%
summarise(mean_dd = mean(dep_delay), sd_dd = sd(dep_delay), n = n())

```
Out[20]:
```

Here, we first grouped the data by `origin`

, and then calculated the summary
statistics.

3.
Calculate the median and interquartile range for `arr_delay`

s of flights in the
`sfo_feb_flights`

data frame, grouped by carrier. Which carrier is the has the hights
IQR of arrival delays?

- American Airlines
- JetBlue Airways
- Virgin America
- Delta and United Airlines
- Frontier Airlines

```
In [66]:
```sfo_feb_flights %>%
group_by(carrier) %>%
summarise(median_dd = median(arr_delay), IQR_dd = IQR(arr_delay)) %>%
arrange(desc(IQR_dd))
# Answer is AA

```
Out[66]:
```

Which month would you expect to have the highest average delay departing from an NYC airport?

Let's think about how we would answer this question:

- First, calculate monthly averages for departure delays. With the new language
we are learning, we need to
`group_by`

months, then`summarise`

mean departure delays.

- Then, we need to
`arrange`

these average delays in`desc`

ending order

```
In [22]:
```nycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay)) %>%
arrange(desc(mean_dd))

```
Out[22]:
```

4. Which month has the highest average departure delay from an NYC airport?

- January
- March
- July
- October
- December

5. Which month has the highest median departure delay from an NYC airport?

- January
- March
- July
- October
- December

```
In [23]:
```nycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay), median_dd = median(dep_delay)) %>%
arrange(desc(median_dd)) # Month 12

```
Out[23]:
```

```
In [64]:
```nycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay), IQR_dd = IQR(dep_delay)) %>%
arrange(desc(IQR_dd)) # Month 12

```
Out[64]:
```

6. Is the mean and the median a more reliable measure for deciding which month(s) to avoid flying if you really dislike delayed flights, and why?

- Mean would be more reliable as it gives us the true average.
- Mean would be more reliable as the distribution of delays is symmetric.
- Median would be more reliable as the distribution of delays is skewed.
- Median would be more reliable as the distribution of delays is symmetric.
- Both give us useful information.

C

```
In [28]:
```ggplot(nycflights, aes(x = factor(month), y = dep_delay)) +
geom_boxplot()

```
```