1 Basic information

This is a list of 6 exercises for the Applied Quantitative Methods with R labs. You can solve these exercises
using base R functionalities or functions from the tidyverse (e.g. dplyr ) package. Solutions should be
send via moodle platform. Outputs are presented in html tables but only for comparison purposes. You do
not need to create html tables. Note that solving some of these exercises requires going through help
pages or looking for an appropriate function in the packages documentation.

Deadline to send solutions is the 9th of January 2023.

If you have questions do not hesitate to contact us via email.

2 Exercise 1 (1 pt)

The sum of the squares of the first ten natural numbers is,

The square of the sum of the first ten natural numbers is,

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the
sum is .

Find the difference between the sum of the squares of the first one hundred natural numbers and the
square of the sum.

Result: -25164150 .

3 Exercise 2 (1 pt)

Write an R program to create a data.frame which contain the following details

employee salary

Jane B 1000

David G 2500

Emilo A 1500

Assignments for extra 10 pts

Maciej Beręsewicz, Tomasz Klimanek, Marcin Szymkowiak

12 + 22+. . . +102 = 385

(1 + 2+. . . +10)2 = 552 = 3025

385 − 3025 = −2640

employee salary

Janet F 3000

George H 680

and display summary of the data.

4 Exercise 3 (1 pt)

Download this dataset. The dataset is about the number of foreigners insured in Poland according to the
ZUS data. It contains the following columns:

kwartal – quarter (format: YYYYQQ, i.e. 2021Q1 refers to 1 quarter of 2021)
obywatelstwo – citizenship (in Polish)
wiek – age group (levels: ogol, 19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-
64, 60+, 65 , where ogol refers to total ),
plec – sex (levels: ogol, kob, mez , where ogol refers to total , kob to females and mez to males ),
ubezp – the number of insured people.

Your task in this assignment consists of two steps:

1. read the data using appropriate function from the readr package or base R (0.5 pt),
2. rename the columns using the following rules (0.5 pt),

kwartal to quarter ,
obywatelstwo to citizenship ,
wiek to age ,
plec to sex ,
ubezp to count .

The expected result is presented below.

quarter citizenship age sex count

2019Q1 ALBAŃSKIE ogol ogol 369

2019Q1 ALGIERSKIE ogol ogol 592

2019Q1 AMERYKAŃSKIE ogol ogol 1792

2019Q1 ANDORSKIE ogol ogol 6

2019Q1 ANGOLSKIE ogol ogol 142

2019Q1 ARGENTYŃSKIE ogol ogol 177



5 Exercise 4 (2 pt)

Create the following data.frame containing information about the overall number of foreigners in Poland
according to ZUS data. Column quarter refers to the quarter column and Freq is based on the count

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