Descriptive Statistics
Additional 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)
number of cars in a household
food type (fruit, meat, vegetable etc.)
highest level of education achieved (1-high school, 2 - first degree, 3 - higher degree).
floor space of a house (in m2 )
2.
A survey is aimed at measuring the support of Polish people for adopting the Euro. A
telephone survey is used based on choosing 1000 numbers at random from the phonebook of
stationary telephone numbers in the Warsaw area. 28% of the respondents answered a short
questionnaire.
a) What is the population?
b) What is the sampling frame?
c) What are the potential sources of bias in this survey?
3.
The mean height of all Polish people is 173cm. The mean height of 100 randomly chosen
students at Wrocław University of Technology is 178cm. Which of these numbers is a
parameter and which is a statistic?
4.
Calculate the i) mean ii) median iii) range, iv) standard deviation, v) interquartile range and
vi) coefficient of variation for the following data.
32, 45, 66, 78, 46, 61, 83, 56, 63
5.
The heights of 30 students were observed. The data are given below (measured in cm). Draw a
histogram for these data
152, 155, 156, 158, 159, 162, 164, 165, 166, 167, 167, 168, 172, 173, 174,
175, 176, 176, 178, 178, 179, 182, 184, 185, 187, 189, 194, 195, 198, 203
6.
The following table illustrates the weight of 200 students.
a) Draw a histogram for these data and comment on the shape
Weight (kg)
[40,50]
(50,60]
(60,70]
(70,80]
(80,90]
(90,100]
(100,110]
(110,120]
Frequency
3
14
48
55
40
27
10
3
b) Estimate the mean and standard deviation of the weight of these students.