Descriptive Statistics Final Project with Python & R

Standard_deviation_diagram

R
Python

Overview

Welcome to the Descriptive Statistics Final Project! In this project, you will demonstrate what you have learned in this course by conducting an experiment dealing with drawing from a deck of playing cards and creating a writeup containing your findings. Be sure to check through the project rubric to self-assess and share with others who will give you feedback.

Questions for Investigation

This experiment will require the use of a standard deck of playing cards. This is a deck of fifty-two cards divided into four suits (spades (♠), hearts (♥), diamonds (♦), and clubs (♣)), each suit containing thirteen cards (Ace, numbers 2-10, and face cards Jack, Queen, and King). You can use either a physical deck of cards for this experiment or you may use a virtual deck of cards such as that found on random.org (http://www.random.org/playing-cards/). For the purposes of this task, assign each card a value: The Ace takes a value of 1, numbered cards take the value printed on the card, and the Jack, Queen, and King each take a value of 10.

First, create a histogram depicting the relative frequencies of the card values.
Now, we will get samples for a new distribution. To obtain a single sample, shuffle your deck of cards and draw three cards from it. (You will be sampling from the deck without replacement.) Record the cards that you have drawn and the sum of the three cards’ values. Repeat this sampling procedure a total of at least thirty times.
Let’s take a look at the distribution of the card sums. Report descriptive statistics for the samples you have drawn. Include at least two measures of central tendency and two measures of variability.
Create a histogram of the sampled card sums you have recorded. Compare its shape to that of the original distribution. How are they different, and can you explain why this is the case?
Make some estimates about values you will get on future draws. Within what range will you expect approximately 90% of your draw values to fall? What is the approximate probability that you will get a draw value of at least 20? Make sure you justify how you obtained your values.

Load the libraries

library(ggplot2)

1	library(ggplot2)

Create card deck

suits <- c("D", "C", "H", "S")
cards <- c("A", as.character(seq(2,10)), "J", "Q", "K")
values <- c(1, 2:9, rep(10, 4))

# Build deck
deck <- expand.grid(cards=cards, suits=suits)
deck$value <- values
deck

suits <- c("D", "C", "H", "S")

cards <- c("A", as.character(seq(2,10)), "J", "Q", "K")

values <- c(1, 2:9, rep(10, 4))

# Build deck

deck <- expand.grid(cards=cards, suits=suits)

deck$value <- values

deck

##    cards suits value
## 1      A     D     1
## 2      2     D     2
## 3      3     D     3
## 4      4     D     4
## 5      5     D     5
## 6      6     D     6
## 7      7     D     7
## 8      8     D     8
## 9      9     D     9
## 10    10     D    10
## 11     J     D    10
## 12     Q     D    10
## 13     K     D    10
## 14     A     C     1
## 15     2     C     2
## 16     3     C     3
## 17     4     C     4
## 18     5     C     5
## 19     6     C     6
## 20     7     C     7
## 21     8     C     8
## 22     9     C     9
## 23    10     C    10
## 24     J     C    10
## 25     Q     C    10
## 26     K     C    10
## 27     A     H     1
## 28     2     H     2
## 29     3     H     3
## 30     4     H     4
## 31     5     H     5
## 32     6     H     6
## 33     7     H     7
## 34     8     H     8
## 35     9     H     9
## 36    10     H    10
## 37     J     H    10
## 38     Q     H    10
## 39     K     H    10
## 40     A     S     1
## 41     2     S     2
## 42     3     S     3
## 43     4     S     4
## 44     5     S     5
## 45     6     S     6
## 46     7     S     7
## 47     8     S     8
## 48     9     S     9
## 49    10     S    10
## 50     J     S    10
## 51     Q     S    10
## 52     K     S    10

## cards suits value

## 1 A D 1

## 2 2 D 2

## 3 3 D 3

## 4 4 D 4

## 5 5 D 5

## 6 6 D 6

## 7 7 D 7

## 8 8 D 8

## 9 9 D 9

## 10 10 D 10

## 11 J D 10

## 12 Q D 10

## 13 K D 10

## 14 A C 1

## 15 2 C 2

## 16 3 C 3

## 17 4 C 4

## 18 5 C 5

## 19 6 C 6

## 20 7 C 7

## 21 8 C 8

## 22 9 C 9

## 23 10 C 10

## 24 J C 10

## 25 Q C 10

## 26 K C 10

## 27 A H 1

## 28 2 H 2

## 29 3 H 3

## 30 4 H 4

## 31 5 H 5

## 32 6 H 6

## 33 7 H 7

## 34 8 H 8

## 35 9 H 9

## 36 10 H 10

## 37 J H 10

## 38 Q H 10

## 39 K H 10

## 40 A S 1

## 41 2 S 2

## 42 3 S 3

## 43 4 S 4

## 44 5 S 5

## 45 6 S 6

## 46 7 S 7

## 47 8 S 8

## 48 9 S 9

## 49 10 S 10

## 50 J S 10

## 51 Q S 10

## 52 K S 10

1. Create a histogram depicting the relative frequencies of the card values

First, create a histogram depicting the relative frequencies of the card values.

ggplot(deck, aes(x=value)) + 
    geom_histogram(binwidth=1, origin=-0.5, col="white", fill="royalblue", alpha=0.5) + 
    labs(x="Value", y="Count", title="Card Value Histogram") +
    scale_x_continuous(breaks = seq(1,10)) +
    theme_bw()

ggplot(deck, aes(x=value)) +

geom_histogram(binwidth=1, origin=-0.5, col="white", fill="royalblue", alpha=0.5) +

labs(x="Value", y="Count", title="Card Value Histogram") +

scale_x_continuous(breaks = seq(1,10)) +

theme_bw()

plot of chunk unnamed-chunk-3

2. Get samples for a new distribution

Now, we will get samples for a new distribution. To obtain a single sample, shuffle your deck of cards and draw three cards from it. (You will be sampling from the deck without replacement.) Record the cards that you have drawn and the sum of the three cards’ values. Repeat this sampling procedure a total of at least thirty times.

df <- c()
for (i in 1:5000) {
    df$value[i] <- sum(sample(deck$value,3,replace = FALSE))
}
samples <- data.frame(df)

df <- c()

for (i in 1:5000) {

df$value[i] <- sum(sample(deck$value,3,replace = FALSE))

}

samples <- data.frame(df)

3. Report descriptive statistics for the samples

Let’s take a look at the distribution of the card sums. Report descriptive statistics for the samples you have drawn. Include at least two measures of central tendency and two measures of variability.

summary(samples)

1	summary(samples)

##      value      
##  Min.   : 3.00  
##  1st Qu.:16.00  
##  Median :20.00  
##  Mean   :19.55  
##  3rd Qu.:23.00  
##  Max.   :30.00

## value

## Min. : 3.00

## 1st Qu.:16.00

## Median :20.00

## Mean :19.55

## 3rd Qu.:23.00

## Max. :30.00

4. Create a histogram of the sampled card sums you have recorded

Create a histogram of the sampled card sums you have recorded. Compare its shape to that of the original distribution. How are they different, and can you explain why this is the case?

ggplot(samples, aes(x=value)) + 
    geom_histogram(binwidth=1, origin=-0.5, col="white", fill="royalblue", alpha=0.5) + 
    labs(x="Value", y="Count", title="3 Card Sum Histogram (n=5000)") +
    theme_bw()

ggplot(samples, aes(x=value)) +

geom_histogram(binwidth=1, origin=-0.5, col="white", fill="royalblue", alpha=0.5) +

labs(x="Value", y="Count", title="3 Card Sum Histogram (n=5000)") +

theme_bw()

plot of chunk unnamed-chunk-6

5. Make some estimates about values you will get on future draws

Make some estimates about values you will get on future draws. Within what range will you expect approximately 90% of your draw values to fall? What is the approximate probability that you will get a draw value of at least 20? Make sure you justify how you obtained your values.

a. Within what range will you expect approximately 90% of your draw values to fall?

quantile(samples$value, probs = seq(.05, .95, 0.9))

1	quantile(samples$value, probs = seq(.05, .95, 0.9))

##  5% 95% 
##  11  28

## 5% 95%

## 11 28

b. Approximate probability that you will get a draw value of at least 20?

Calculate the z score

$Z=\frac{X-\mu}{\sigma}$

atleast <- 20
mean <- mean(samples$value)
sd <- sd(samples$value)
z <- (atleast-mean)/sd
z

atleast <- 20

mean <- mean(samples$value)

sd <- sd(samples$value)

z <- (atleast-mean)/sd

## [1] 0.08467613

1 2	## [1] 0.08467613

We could lookup the value in the Z score table, but I want to calculate it.

Convert the Z score to a p-value with the Cumulative Distribution Function. We want to find the probability is larger than the given number so we use the lower.tail=FALSE.

$F(x) = 1 - P(X <= x)$

cdf <- pnorm(z, lower.tail=FALSE)
cdf

1 2	cdf <- pnorm(z, lower.tail=FALSE) cdf

## [1] 0.4662594

1 2	## [1] 0.4662594

As we can see the probability that we will get a draw value of at least 20 is 0.4662594.

Check it out on github Last updated: 31/05/2020 07:29:17

John

I’m creative, imaginative, free-thinking, daydreamer and strategic who needs freedom, peace and space to brainstorm and to fantasize about new and surprising solutions. Generates ideas and solves difficult problems, sees all options, judges accurately and wants to get to the bottom of things.

Interested in Data Science, Data Analytics, Running, Crossfit, Obstacle Running and Coffee.

Tags: Courses, jupyter, notebook, python, R, stats, udacity

7 comments on “Descriptive Statistics Final Project with Python & R”

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George says:

August 21, 2016 at 09:56

Since R vectors can not contain data of the different types:
this
cards <- c("A", as.character(seq(2,10)), "J", "Q", "K")
is equal to this
cards <- c("A", 2:10, "J", "Q", "K")
1. jletteboer says:
  
  August 21, 2016 at 10:13
  
  Hi George, that’s also possible, thanks for the mention.
Mirek says:

August 21, 2016 at 13:44

Good intro to descriptive statistics in R…just one comment.

In the case of your first plot, I believe your aesthetics should be ‘X=value’ not ‘x=values’ …

ggplot(deck, aes(x=values))

…since that is how you named it when building the deck:

deck$value <- values

but I may be wrong 🙂
1. jletteboer says:
  
  August 22, 2016 at 15:43
  
  Hi Mirek,
  
  You’re right, it’s not correct. In this case it works because the values will iterate over the data in the deck and stays the same.
  
  I’ve changed my code.
  
  Thanks for the mention 🙂

Comments are closed.

Descriptive Statistics Final Project with Python & R

Overview

Questions for Investigation

Load the libraries

Create card deck

1. Create a histogram depicting the relative frequencies of the card values

2. Get samples for a new distribution

3. Report descriptive statistics for the samples

4. Create a histogram of the sampled card sums you have recorded

5. Make some estimates about values you will get on future draws

a. Within what range will you expect approximately 90% of your draw values to fall?

b. Approximate probability that you will get a draw value of at least 20?

Like this:

7 comments on “Descriptive Statistics Final Project with Python & R”

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Descriptive Statistics Final Project with Python & R

Overview

Questions for Investigation

Load the libraries

Create card deck

1. Create a histogram depicting the relative frequencies of the card values

2. Get samples for a new distribution

3. Report descriptive statistics for the samples

4. Create a histogram of the sampled card sums you have recorded

5. Make some estimates about values you will get on future draws

a. Within what range will you expect approximately 90% of your draw values to fall?

b. Approximate probability that you will get a draw value of at least 20?

Share this:

Like this:

7 comments on “Descriptive Statistics Final Project with Python & R”

Related Posts

Developing Data Products

Analysing your Apple Health Data with Splunk

Visualizing with D3 JavaScript Network Graphs from R

Titanic – Machine Learning from Disaster (Part 1)