13.1.1 Seminar 1.1 assignments
Problem 1
In a sample of women, the number of children that each woman has, is an example
of which type of measurement?
a. Nominal
b. Ordinal
c. Interval
d. Ratio
Answer:
Nominal and Ordinal are qualitative variables and Interval and Ratio are quantitative
variables. The number of children that each woman has in a sample of women is a
quantitative variable. The difference between the amount of children between the
individual women can also be measured, so it has to be Interval or Ratio. The
difference between Interval and Ratio is that Ratio has an absolute zero while
Interval does not. Since the minimum amount of children a woman can have is zero,
the type of measurement is Ratio.
Problem 2
In which situation would the median be an appropriate measure of central tendency?
a. When the average is not appropriate
b. When the mode is less than 10
c. When the data are of nominal scale level
d. When the data are of ordinal scale level
Answer:
The median would be an appropriate measure of central tendency when the data are
of ordinal scale level. The data are then ordered which is crucial for the median.
Problem 3
Which of the following is not true for a normal distribution?
a. Median is equal to the mode
b. Mode is equal to the mean
c. The distribution is skewed to the right
d. Approximately 95% of the observations are located between the mean minus two
times the standard deviation and the means plus two times the standard deviation
Answer:
In a normal distribution, the mean, mode and median are equal to each other. This
means that options a and b are correct. Option d is also correct, approximately 95%
of the observations are located between the mean minus two times the standard
deviation and the means plus two times the standard deviation. Option c is incorrect,
one of the key features of a normal distribution is that it is symmetrical.
Problem 4
,Which of the following is true for a distribution skewed to the left?
a. Mean is smaller than the median, the median is smaller than the mode
b. Mode is smaller than the median, the median is smaller than the mean
c. Mode, median and mean are equal
d. Median is smaller than the mean, the mean is smaller than the mode
Answer:
In a distribution skewed to the left;
Mean < Median < Mode
Problem 5
Which of the following is true of a normal distribution?
a. The distribution has two modes
b. The distribution is not symmetric
c. Approximately 68% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation
d. Approximately 50% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation
Answer:
A normal distribution has only one mode. A normal distribution is symmetrical.
Approximately 68% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation.
Problem 6
Which option is the mean of the numbers below?
4 5 4 4 3 5 6 3 4 2
a. 10
b. 8
c. 4
d. 4.5
Answer:
If you add up all the numbers below (4+5+4+4+3+5+6+3+4+2), the sum is 40. There
are in total 10 numbers. To calculate the mean, the sum of the numbers has to be
divided by the number of data points. 40 divided by 10 is 4.
Problem 7
Which option is the variance of the numbers below?(For this question more than one
answers might be correct)
4 5 4 4 3 5 6 3 4 2
a. 4.00
b. 1.33
, c. 1.20
d. 1.80
Answer:
To calculate the variance, the mean should first be calculated. The mean is the sum
divided by the amount of numbers. The sum is 40 (4+5+4+4+3+5+6+3+4+2) and the
amount of numbers is 10. 40 divided by 10 is 4, which means that the mean is 4. The
mean is then subtracted from each number (0 1 0 0 -1 1 2 -1 0 -2) The difference
which is left is then squared. The sum of these numbers is then again divided by 10.
The sum of these numbers is 12. 12 divided by 10 is 1.20.
Problem 8
If the variance is very low:
a. The individuals in the data set are very different from each other
b. The standard deviation is 0
c. The data set is too small
d. The individuals in the data set are very similar to each other
Answer:
Variance measures how far a set of data is spread out. A low variance indicates that
all of the data values are identical. A small or low variance indicates that the data
points tend to be very close to the mean and to each other.
Problem 9
What is the minimal level of measurement required to calculate a mode?
a. ratio
b. interval
c. ordinal
d. nominal
Answer:
The mode is used with nominal-level data, as it is the only measure of central
tendency available for such variables.
Problem 10
Explain on what scale level the following measurements are:
a. Hair colour (e.g. brown, black, blond, red, grey)
b. Social economic status (low, middle, high)
c. Income (in euros)
d. Temperature (in degrees Celsius)
e. Age (in years)
f. Blood pressure (in mmHg)
g. Sort of cancer (lung, prostate, bowel, etc.)
Problem 1
In a sample of women, the number of children that each woman has, is an example
of which type of measurement?
a. Nominal
b. Ordinal
c. Interval
d. Ratio
Answer:
Nominal and Ordinal are qualitative variables and Interval and Ratio are quantitative
variables. The number of children that each woman has in a sample of women is a
quantitative variable. The difference between the amount of children between the
individual women can also be measured, so it has to be Interval or Ratio. The
difference between Interval and Ratio is that Ratio has an absolute zero while
Interval does not. Since the minimum amount of children a woman can have is zero,
the type of measurement is Ratio.
Problem 2
In which situation would the median be an appropriate measure of central tendency?
a. When the average is not appropriate
b. When the mode is less than 10
c. When the data are of nominal scale level
d. When the data are of ordinal scale level
Answer:
The median would be an appropriate measure of central tendency when the data are
of ordinal scale level. The data are then ordered which is crucial for the median.
Problem 3
Which of the following is not true for a normal distribution?
a. Median is equal to the mode
b. Mode is equal to the mean
c. The distribution is skewed to the right
d. Approximately 95% of the observations are located between the mean minus two
times the standard deviation and the means plus two times the standard deviation
Answer:
In a normal distribution, the mean, mode and median are equal to each other. This
means that options a and b are correct. Option d is also correct, approximately 95%
of the observations are located between the mean minus two times the standard
deviation and the means plus two times the standard deviation. Option c is incorrect,
one of the key features of a normal distribution is that it is symmetrical.
Problem 4
,Which of the following is true for a distribution skewed to the left?
a. Mean is smaller than the median, the median is smaller than the mode
b. Mode is smaller than the median, the median is smaller than the mean
c. Mode, median and mean are equal
d. Median is smaller than the mean, the mean is smaller than the mode
Answer:
In a distribution skewed to the left;
Mean < Median < Mode
Problem 5
Which of the following is true of a normal distribution?
a. The distribution has two modes
b. The distribution is not symmetric
c. Approximately 68% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation
d. Approximately 50% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation
Answer:
A normal distribution has only one mode. A normal distribution is symmetrical.
Approximately 68% of the observations are located between the mean minus one
standard deviation and the mean plus one standard deviation.
Problem 6
Which option is the mean of the numbers below?
4 5 4 4 3 5 6 3 4 2
a. 10
b. 8
c. 4
d. 4.5
Answer:
If you add up all the numbers below (4+5+4+4+3+5+6+3+4+2), the sum is 40. There
are in total 10 numbers. To calculate the mean, the sum of the numbers has to be
divided by the number of data points. 40 divided by 10 is 4.
Problem 7
Which option is the variance of the numbers below?(For this question more than one
answers might be correct)
4 5 4 4 3 5 6 3 4 2
a. 4.00
b. 1.33
, c. 1.20
d. 1.80
Answer:
To calculate the variance, the mean should first be calculated. The mean is the sum
divided by the amount of numbers. The sum is 40 (4+5+4+4+3+5+6+3+4+2) and the
amount of numbers is 10. 40 divided by 10 is 4, which means that the mean is 4. The
mean is then subtracted from each number (0 1 0 0 -1 1 2 -1 0 -2) The difference
which is left is then squared. The sum of these numbers is then again divided by 10.
The sum of these numbers is 12. 12 divided by 10 is 1.20.
Problem 8
If the variance is very low:
a. The individuals in the data set are very different from each other
b. The standard deviation is 0
c. The data set is too small
d. The individuals in the data set are very similar to each other
Answer:
Variance measures how far a set of data is spread out. A low variance indicates that
all of the data values are identical. A small or low variance indicates that the data
points tend to be very close to the mean and to each other.
Problem 9
What is the minimal level of measurement required to calculate a mode?
a. ratio
b. interval
c. ordinal
d. nominal
Answer:
The mode is used with nominal-level data, as it is the only measure of central
tendency available for such variables.
Problem 10
Explain on what scale level the following measurements are:
a. Hair colour (e.g. brown, black, blond, red, grey)
b. Social economic status (low, middle, high)
c. Income (in euros)
d. Temperature (in degrees Celsius)
e. Age (in years)
f. Blood pressure (in mmHg)
g. Sort of cancer (lung, prostate, bowel, etc.)
