STA1501/201/0/20
23
Tutorial Letter 201/0/2023
Descriptive Statistics and Probability
STA1501
Year module
Department of Statistics
Solutions to Assignment 1
BAR CODE
university
Learn without limits.
Open Rubric of south africa
, ASSIGNMENT 01
Unique Nr.: 806739
Fixed closing date: 02 July 2021
PART A: 20 Marks (1 mark each)
QUESTION 1
False. A qualitative variable for which there is some kind of ranking for the different
values is called an ordinal variable.
QUESTION 2
False. Samples in which the elements to be selected are drawn on the basis of
probabilities in such a way that each element in the population has the same
probability of being selected as part of the sample are called simple random
samples. These fall under under probability sampling methods, but there are others.
QUESTION 3
True. Each individual data value is split into a stem and leaf. For example, suppose
there exist individual data values as follows:
150, 155, 156, 200, 218, 211, and 216.
Then the stem-and-leaf display is
Stem Leaf
15 0 5 6
20 0
21 1 6 8
and from this, all of the original data valus can be read out.
QUESTION 4
False. This would be an example of a statistic.
QUESTION 5
False. A histogram is used to summarise only quantitative data.
QUESTION 6
False. The interquartile range tells us the spread of the middle half of a dataset,
whereas; the range tells the spread of the entire dataset. The length of the first does
not have to be half of the second, that depends entirely on how the data is spread
around.
2
, STA1501/20
1
QUESTION 7
False.
QUESTION 8
False. Increasing the sample size has a property of making the sample statistic less
variable. This has no influence on survey bias and thus a large sample size does not
correct methodological problems (i.e., bias, undercoverage and etc.).
QUESTION 9
True, since b0 = 5.2 and b1 =0.3. If b1 < 0, then x and y have a negative relationship, and
otherwise if b1—> 0, then x and y have a positive relationship.
QUESTION 10
Sxy
False. Since r= , then xy
S can be smaller or greater than r.
Sy Sx
QUESTION 11
True, for example, a data set of a sample of 10 records: 9 8 4 6 7 8 6 9 5 3 .
The mode of the data set is 6, 8 and 9.
QUESTION 12
False, This is only true when the frequency of the data is odd number of values. If
there is an even number of values the median is the average of the two middle
values which might not be an original number.
QUESTION 13
False. Box plot requires the median, rather than the mean, as follows.
3
23
Tutorial Letter 201/0/2023
Descriptive Statistics and Probability
STA1501
Year module
Department of Statistics
Solutions to Assignment 1
BAR CODE
university
Learn without limits.
Open Rubric of south africa
, ASSIGNMENT 01
Unique Nr.: 806739
Fixed closing date: 02 July 2021
PART A: 20 Marks (1 mark each)
QUESTION 1
False. A qualitative variable for which there is some kind of ranking for the different
values is called an ordinal variable.
QUESTION 2
False. Samples in which the elements to be selected are drawn on the basis of
probabilities in such a way that each element in the population has the same
probability of being selected as part of the sample are called simple random
samples. These fall under under probability sampling methods, but there are others.
QUESTION 3
True. Each individual data value is split into a stem and leaf. For example, suppose
there exist individual data values as follows:
150, 155, 156, 200, 218, 211, and 216.
Then the stem-and-leaf display is
Stem Leaf
15 0 5 6
20 0
21 1 6 8
and from this, all of the original data valus can be read out.
QUESTION 4
False. This would be an example of a statistic.
QUESTION 5
False. A histogram is used to summarise only quantitative data.
QUESTION 6
False. The interquartile range tells us the spread of the middle half of a dataset,
whereas; the range tells the spread of the entire dataset. The length of the first does
not have to be half of the second, that depends entirely on how the data is spread
around.
2
, STA1501/20
1
QUESTION 7
False.
QUESTION 8
False. Increasing the sample size has a property of making the sample statistic less
variable. This has no influence on survey bias and thus a large sample size does not
correct methodological problems (i.e., bias, undercoverage and etc.).
QUESTION 9
True, since b0 = 5.2 and b1 =0.3. If b1 < 0, then x and y have a negative relationship, and
otherwise if b1—> 0, then x and y have a positive relationship.
QUESTION 10
Sxy
False. Since r= , then xy
S can be smaller or greater than r.
Sy Sx
QUESTION 11
True, for example, a data set of a sample of 10 records: 9 8 4 6 7 8 6 9 5 3 .
The mode of the data set is 6, 8 and 9.
QUESTION 12
False, This is only true when the frequency of the data is odd number of values. If
there is an even number of values the median is the average of the two middle
values which might not be an original number.
QUESTION 13
False. Box plot requires the median, rather than the mean, as follows.
3
