MSDS Spring 2018
DATA 606 Statistics and Probability for Data Analytics
Jiadi Li
Lab 0: Introduction to R and RStudio
source("http://www.openintro.org/stat/data/arbuthnot.R")The Data: Dr. Arbuthnot’s Baptism Records
The Arbuthnot data set refers to Dr. John Arbuthnot, an 18th century physician, writer, and mathematician. He was interested in the ratio of newborn boys to newborn girls, so he gathered the baptism records for children born in London for every year from 1629 to 1710. We can take a look at the data by typing its name into the console.
arbuthnot## year boys girls
## 1 1629 5218 4683
## 2 1630 4858 4457
## 3 1631 4422 4102
## 4 1632 4994 4590
## 5 1633 5158 4839
## 6 1634 5035 4820
## 7 1635 5106 4928
## 8 1636 4917 4605
## 9 1637 4703 4457
## 10 1638 5359 4952
## 11 1639 5366 4784
## 12 1640 5518 5332
## 13 1641 5470 5200
## 14 1642 5460 4910
## 15 1643 4793 4617
## 16 1644 4107 3997
## 17 1645 4047 3919
## 18 1646 3768 3395
## 19 1647 3796 3536
## 20 1648 3363 3181
## 21 1649 3079 2746
## 22 1650 2890 2722
## 23 1651 3231 2840
## 24 1652 3220 2908
## 25 1653 3196 2959
## 26 1654 3441 3179
## 27 1655 3655 3349
## 28 1656 3668 3382
## 29 1657 3396 3289
## 30 1658 3157 3013
## 31 1659 3209 2781
## 32 1660 3724 3247
## 33 1661 4748 4107
## 34 1662 5216 4803
## 35 1663 5411 4881
## 36 1664 6041 5681
## 37 1665 5114 4858
## 38 1666 4678 4319
## 39 1667 5616 5322
## 40 1668 6073 5560
## 41 1669 6506 5829
## 42 1670 6278 5719
## 43 1671 6449 6061
## 44 1672 6443 6120
## 45 1673 6073 5822
## 46 1674 6113 5738
## 47 1675 6058 5717
## 48 1676 6552 5847
## 49 1677 6423 6203
## 50 1678 6568 6033
## 51 1679 6247 6041
## 52 1680 6548 6299
## 53 1681 6822 6533
## 54 1682 6909 6744
## 55 1683 7577 7158
## 56 1684 7575 7127
## 57 1685 7484 7246
## 58 1686 7575 7119
## 59 1687 7737 7214
## 60 1688 7487 7101
## 61 1689 7604 7167
## 62 1690 7909 7302
## 63 1691 7662 7392
## 64 1692 7602 7316
## 65 1693 7676 7483
## 66 1694 6985 6647
## 67 1695 7263 6713
## 68 1696 7632 7229
## 69 1697 8062 7767
## 70 1698 8426 7626
## 71 1699 7911 7452
## 72 1700 7578 7061
## 73 1701 8102 7514
## 74 1702 8031 7656
## 75 1703 7765 7683
## 76 1704 6113 5738
## 77 1705 8366 7779
## 78 1706 7952 7417
## 79 1707 8379 7687
## 80 1708 8239 7623
## 81 1709 7840 7380
## 82 1710 7640 7288Some Exploration
Let’s start to examine the data a little more closely. We can access the data in a single column of a data frame separately using a command like
arbuthnot$boys## [1] 5218 4858 4422 4994 5158 5035 5106 4917 4703 5359 5366 5518 5470 5460
## [15] 4793 4107 4047 3768 3796 3363 3079 2890 3231 3220 3196 3441 3655 3668
## [29] 3396 3157 3209 3724 4748 5216 5411 6041 5114 4678 5616 6073 6506 6278
## [43] 6449 6443 6073 6113 6058 6552 6423 6568 6247 6548 6822 6909 7577 7575
## [57] 7484 7575 7737 7487 7604 7909 7662 7602 7676 6985 7263 7632 8062 8426
## [71] 7911 7578 8102 8031 7765 6113 8366 7952 8379 8239 7840 7640This command will only show the number of boys baptized each year.
- What command would you use to extract just the counts of girls baptized? Try it!
arbuthnot$girls## [1] 4683 4457 4102 4590 4839 4820 4928 4605 4457 4952 4784 5332 5200 4910
## [15] 4617 3997 3919 3395 3536 3181 2746 2722 2840 2908 2959 3179 3349 3382
## [29] 3289 3013 2781 3247 4107 4803 4881 5681 4858 4319 5322 5560 5829 5719
## [43] 6061 6120 5822 5738 5717 5847 6203 6033 6041 6299 6533 6744 7158 7127
## [57] 7246 7119 7214 7101 7167 7302 7392 7316 7483 6647 6713 7229 7767 7626
## [71] 7452 7061 7514 7656 7683 5738 7779 7417 7687 7623 7380 7288- Is there an apparent trend in the number of girls baptized over the years?
How would you describe it?
While there are flutuations, the girl population is increasing overall. Worth noticing, there is an obvious decrease from 1640 to 1650.
- Now, make a plot of the proportion of boys over time. What do you see?
plot(x = arbuthnot$year, y = arbuthnot$boys/(arbuthnot$boys+arbuthnot$girls), type = "l")
On Your Own
In the previous few pages, you recreated some of the displays and preliminary analysis of Arbuthnot’s baptism data. Your assignment involves repeating these steps, but for present day birth records in the United States. Load up the present day data with the following command.
source("http://www.openintro.org/stat/data/present.R")The data are stored in a data frame called present.
- What years are included in this data set? What are the dimensions of the data frame and what are the variable or column names?
summary(present)## year boys girls
## Min. :1940 Min. :1211684 Min. :1148715
## 1st Qu.:1956 1st Qu.:1799857 1st Qu.:1711405
## Median :1971 Median :1924868 Median :1831679
## Mean :1971 Mean :1885600 Mean :1793915
## 3rd Qu.:1986 3rd Qu.:2058524 3rd Qu.:1965538
## Max. :2002 Max. :2186274 Max. :2082052dim(present)## [1] 63 3summary(arbuthnot)## year boys girls
## Min. :1629 Min. :2890 Min. :2722
## 1st Qu.:1649 1st Qu.:4759 1st Qu.:4457
## Median :1670 Median :6073 Median :5718
## Mean :1670 Mean :5907 Mean :5535
## 3rd Qu.:1690 3rd Qu.:7576 3rd Qu.:7150
## Max. :1710 Max. :8426 Max. :7779- What years are included in this data set? What are the dimensions of the data frame and what are the variable or column names?
The years included in present dataset are from 1940 to 2002. The dimension is 63 (rows, or records) x 3 (columns, or variables). Variables are also year, boys and girls.
- How do these counts compare to Arbuthnot’s? Are they on a similar scale?
There are There are much more newborns in years of 1940 to 2002 for both boys and girls.
- Make a plot that displays the boy-to-girl ratio for every year in the data set. What do you see? Does Arbuthnot’s observation about boys being born in greater proportion than girls hold up in the U.S.? Include the plot in your response.
plot(x = present$year, y = present$boys/present$girls, type = "l")
Boy-to-girl ratio is over 1 for every year showing that more boys than girls are born each year all the time. However, it’s also noticable that the ratio, while not constant, showing a decreasing trend overtime.
- In what year did we see the most total number of births in the U.S.? You cancrefer to the help files or the R reference card http://cran.r-project.org/doc/contrib/Short-refcard.pdf to find helpful commands.
plot(x = present$year, y = present$boys+present$girls, type = "h")
max_population <- max(present$boys+present$girls)
max_population## [1] 4268326present$year[present$boys+present$girls == max_population]## [1] 1961Baed on both numerical and graphical representation of the dataset, the highest population happend in 1961 with a total number of births of 4,268,326.