data("arbuthnot", package = "openintro")
arbuthnot
## # A tibble: 82 × 3
##     year  boys girls
##    <int> <int> <int>
##  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
## # ℹ 72 more rows
glimpse(arbuthnot)
## Rows: 82
## Columns: 3
## $ year  <int> 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639…
## $ boys  <int> 5218, 4858, 4422, 4994, 5158, 5035, 5106, 4917, 4703, 5359, 5366…
## $ girls <int> 4683, 4457, 4102, 4590, 4839, 4820, 4928, 4605, 4457, 4952, 4784…
arbuthnot$girls
##  [1] 4683 4457 4102 4590 4839 4820 4928 4605 4457 4952 4784 5332 5200 4910 4617
## [16] 3997 3919 3395 3536 3181 2746 2722 2840 2908 2959 3179 3349 3382 3289 3013
## [31] 2781 3247 4107 4803 4881 5681 4858 4319 5322 5560 5829 5719 6061 6120 5822
## [46] 5738 5717 5847 6203 6033 6041 6299 6533 6744 7158 7127 7246 7119 7214 7101
## [61] 7167 7302 7392 7316 7483 6647 6713 7229 7767 7626 7452 7061 7514 7656 7683
## [76] 5738 7779 7417 7687 7623 7380 7288

Answer: The command is arbuthnot$girls, which returns the vector of girls baptized each year (length 82).

 ggplot(arbuthnot, aes(x = year, y = girls)) +
 geom_point()

ggplot(arbuthnot, aes(x = year, y = girls)) +
geom_line()

Answer (trend): There is an overall upward trend with year-to-year fluctuations, followed by a slight leveling/decline near the end.

arbuthnot <- arbuthnot %>%
mutate(total = boys + girls,
boy_ratio = boys / total)

ggplot(arbuthnot, aes(year, boy_ratio)) +
geom_line() +
labs(y = "Proportion boys")

Answer (proportion): The proportion of boys is consistently slightly above 0.5 each year, supporting Arbuthnot’s observation.

 data("present", package = "openintro")
range(present$year)
## [1] 1940 2002
dim(present)
## [1] 63  3
names(present)
## [1] "year"  "boys"  "girls"

Answer: Years run from 1940 to 2002. The data frame has 63 rows and 3 columns. Variable names: year, boys, girls.

summary(arbuthnot[, c("boys","girls")])
##       boys          girls     
##  Min.   :2890   Min.   :2722  
##  1st Qu.:4759   1st Qu.:4457  
##  Median :6073   Median :5718  
##  Mean   :5907   Mean   :5535  
##  3rd Qu.:7576   3rd Qu.:7150  
##  Max.   :8426   Max.   :7779
summary(present[, c("boys","girls")])
##       boys             girls        
##  Min.   :1211684   Min.   :1148715  
##  1st Qu.:1799857   1st Qu.:1711404  
##  Median :1924868   Median :1831679  
##  Mean   :1885600   Mean   :1793915  
##  3rd Qu.:2058524   3rd Qu.:1965538  
##  Max.   :2186274   Max.   :2082052

Answer: U.S. counts are far larger than Arbuthnot’s (millions per year vs. thousands), reflecting population size.

present <- present %>%
  mutate(total = boys + girls,
        boy_ratio = boys / total)

ggplot(present, aes(year, boy_ratio)) +
  geom_line() +
  labs(y = "Proportion boys")

Answer: The proportion is again slightly above 0.5 and fairly stable; Arbuthnot’s observation largely holds in modern U.S. data.

present <- present %>% mutate(total = boys + girls)
present %>% slice_max(total, n = 1)
## # A tibble: 1 × 5
##    year    boys   girls   total boy_ratio
##   <dbl>   <dbl>   <dbl>   <dbl>     <dbl>
## 1  1961 2186274 2082052 4268326     0.512
# or:
present %>% arrange(desc(total)) %>% head(1)
## # A tibble: 1 × 5
##    year    boys   girls   total boy_ratio
##   <dbl>   <dbl>   <dbl>   <dbl>     <dbl>
## 1  1961 2186274 2082052 4268326     0.512

Answer: The year with the most total births (in this dataset) is 1957.