1.2 Solutions

1.2.1 Exercise 3

Calculate the square root of 1369 using the sqrt() function.

sqrt(1369)
[1] 37

1.2.2 Exercise 4

Square the number 13 using the ^ operator.

13^2
[1] 169

1.2.3 Exercise 5

What is the result of summing all numbers from 1 to 100?

# sequence of numbers from 1 to 100 in steps of 1
numbers_1_to_100 <- seq(from = 1, to = 100, by = 1)
# sum over the vector
result <- sum(numbers_1_to_100)
# print the result
result
[1] 5050
# alternative solution
result <- sum(1:100)

The result is 5050.

1.2.4 Exercise 6

Using the London borough data, create a CSV file that contains the following columns:

  • The names of the London Boroughs

  • Population change between 1811 and 1911

  • Population change between 1911 and 1961

  • Population change 1961 and 2011

# First we load the dataset (if you haven't done it already)

pop <- read.csv("https://data.london.gov.uk/download/historic-census-population/2c7867e5-3682-4fdd-8b9d-c63e289b92a6/census-historic-population-borough.csv")

# Now we select the variables to use for the new dataset. Note that I am using a mathematical function (substracting) within the data.frame() function. This way, I can get the population changes.

pop_new <- data.frame(pop$Area.Name, pop$Persons.1911-pop$Persons.1811, pop$Persons.1961-pop$Persons.1911, pop$Persons.2001-pop$Persons.1961)

# Now we change the names of the columns with the colnames() functions

colnames(pop_new) <- c("London_Borough", "Change_1911_1811", "Change_1961_1911", "Change_2001_1961")

1.2.5 Exercise 7

Which Boroughs had the fastest growth during the 19th Century, and which had the slowest?

# We can use the arrange() function to sort the 
library(tidyverse)

pop_sorted <- arrange(pop_new, 
                      desc(Change_1911_1811)) # use desc() to make it descending order

# most growth
head(pop_sorted) 
  London_Borough Change_1911_1811 Change_1961_1911 Change_2001_1961
1 Greater London          5859000           835094          -825037
2   Inner London          3893000         -1509119          -726816
3   Outer London          1967000          2344213           -98221
4      Southwark           440000          -265587           -68546
5         Newham           417000          -161612           -21504
6  Tower Hamlets           390000          -364318            -9599
# least growth
tail(pop_sorted)
         London_Borough Change_1911_1811 Change_1961_1911 Change_2001_1961
31               Sutton            49000           115095            10672
32               Harrow            37000           167080            -2258
33 Barking and Dagenham            35000           138092           -13148
34           Hillingdon            27000           190370            14636
35             Havering            26000           212598           -21336
36       City of London          -101000           -15233             2414

The smallest growth (it is actually negative) is from the City of London, while the largest growth was in Southwark. Note, of course, that ‘Greater’, ‘Inner’ and ‘Outer’ are not boroughs.