Descriptive Statistics
Tutorial Sheet 1
1.
Classify the following variables according to whether they are i) qualitative ii) quantitative.
Further classify the qualitative variables into nominal and ordinal variables and the
quantitative variables into discrete and continuous
a)
b)
c)
d)
energy consumption ratings (A – E)
industrial sector (retail, manufacture, public, etc.)
temperature
number of telephones owned by a household
2.
A survey is aimed at measuring how much exercise adults in Poland take. A list of households
to survey was chosen at random. At most one individual was interviewed from each
household. Interviewers visited households in the evenings or at weekends and interviews
were carried out at the homes of the interviewee. If the interviewer visited a house twice, but
found no-one at home, then no interview was carried out. The interview included questions on
how often people exercised and for how long.
a) What is the population?
b) What is the sampling frame?
c) What are the potential sources of bias in this survey?
3.
In the last election 12% of the eligible voters voted for Kukiz. In a survey of 4000 people
made before the election, 15% said that they would vote for Kukiz. Is 12% a statistic or a
parameter? Is 15% a statistic or a parameter?
4.
Calculate the i) mean ii) median iii) range, iv) standard deviation, v) interquartile range and
vi) coefficient of variation for the following data.
5, 8, 7, 11, 9, 7, 11, 14
5.
The weights of 20 students were observed. The data are given below (measured in kg). Draw a
histogram for these data
52, 55, 56, 59, 62, 65, 66, 68, 72, 74,
75, 76, 78, 79, 82, 84, 85, 89, 94, 98
6.
The monthly earnings of 300 employees were observed (in Euro). The results are presented in
the form of a table below. Draw a histogram for these data and comment on its shape.
Earnings
[0, 1000]
(1000,2000]
(2000,3000]
(3000,4000]
(4000,5000]
(5000,6000]
(6000,7000]
(7000,8000]
Frequency
30
140
70
35
15
6
3
1