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BBS1003 Statistics Course Summary All seminars
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BBS1003 Statistics Course Summary All seminars
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Seminar 1.1 assignmentsStatistical concepts to be discussed: level of measurement, measures of central tendency,
measures of variability, normal distribution, skewness, bar chart, histogram, frequency table,
box plot.
Don’t forget watching the videos!
1. Problem
Given. A study where the variable gender (female/non-binary/male) is studied.
Question. What is the level of measurement of the variable gender (female/non-
binary/male)?
Categoric nominal variable. (there is no rank so not ordinal)
2. Problem
Given. A median.
Question. In which situation would the median be an appropriate measure of central
tendency?
(a) When the data are of nominal scale level
(b) When the average is not appropriate
If the average is not appropriate due to outliers, then the median can be used as
this measure of central tendency is not sensitive to outliers.
(c) When the data are of ordinal scale level
Yes, you can order them from small to large, so it is possible to find the middle.
(d) When there are two modes
Median is computable.
3. Problem
Given. A normal distribution.
Question. What is a characteristic of a normal distribution?
(a) Approximately 99% of the observations are located between the mean minus
three times the standard deviation and the mean plus three times the standard
deviation
Following the 68/95/99.7% rule, which is a characteristic of normal distribution,
the occurrence described is the 99.7% part of the rule.
(b) The distribution is skewed to the left
(c) The distribution has two modes
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, (d) The distribution is skewed to the right
4. Problem
Given. A distribution skewed to the left.
Question. What is a characteristic of a distribution skewed to the left?
(a) Median is smaller than the mean, the mean is smaller than the mode
(b) Mode, median and mean are equal
(c) Mean is smaller than the median, the median is smaller than the mode
Skewed distribution to the left is a negative skew, in which mean < median <
mode.
(d) Mode is smaller than the median, the median is smaller than the mean
5. Problem
Given. A normal distribution.
Question. What is a characteristic of a normal distribution?
(a) Approximately 50% of the observations are smaller than the mean
Following the 68/95/99.7% rule, at 3 standard deviations 99.7% is covered
(greater and lesser than the mean), and since the distribution is symmetrical,
roughly 50% is greater and 50% is lesser than the mean.
(b) Approximately 99% of the observations are located between the mean minus
two standard deviations and the mean plus two standard deviations
(c) The mean is lower than the mode, the mode is lower than the median
(d) The distribution is not symmetric
6. Problem
Given. The grades of 11 students (/10) are given below
7 7 10 9 7 1 2 9 2 4 10
Question. What is the value of the mean?
(a) 5.2
(b) 7.2
(c) 6.2
(d) 11.4
7. Problem
Given. The grades of 13 students (/10) are given below
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, 6 8 4 1 3 6 2 7 6 10 4 6 2
1 2 2 3 4 4 6 6 6 6 7 8 10
Question. What is the variance? (For this question more than one answers might be
correct)
The mean is 5.
Variance (population): ((1-5)2 + (2-5)2 + (2-5)2 ….. )/13 (divided by n)
Variance (sample): …../13- 1, so divided by 12 (divided by n-1)
(a) 6.3 population
(b) 6.4
(c) 6.7
(d) 6.8 sample
8. Problem
Given. A sample with very low variance.
Question. What does a very low variance mean?
(a) The individuals in the data set are homogeneous
Low variance means that the distribution is not very large. This means that the
data of the individuals does not differ that much, therefore is they are
homogenous.
(b) The individuals in the data set are very different from each other
(c) The standard deviation is large (no since SD is the square root of variance,
proportional relation)
(d) The sample size is small
9. Problem
Given. One mode.
Question. What is the minimal level of measurement required to calculate a mode?
Aren’t they all possible to calculate a mode?
(a) Ratio
(b) ordinal
(c) Interval
(d) Nominal, you cannot actually order them, but is it possible to look for the
highest frequency, which is the minimum requirement (no numbers, rank etc.
needed to calculate the mode) (all others possible to calculate the mode).
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, 10. Problem
Given. A variable Blood pressure (in mmHg).
Question. What is the level of measurement of the variable Blood pressure (in mmHg)?
Numerical ratio/continuous variable.
Blood pressure is systolic over diastolic pressure, and in both cases there is a true zero.
Nominal, ordinal, ratio or interval is more precise, whereas discreet and continuous is
more general.
11. Problem
Given. Consider 7 persons having the following (monthly) salaries (in euros):
1900 1800 2500 2000 2200 1700 1900
Question.
(a) What is the mean?
Mean: 2000
(b) What is the median?
1700 1800 1900 1900 2000 2200 2500
Median: 1900
(c) What is the mode?
Mode: 1900
12. Problem
Given. Consider 7 persons having the following (monthly) salaries (in euros):
1900 2500 2000 2200 1700 1900 19000
Question.
(a) What is the mean?
Mean: 4457
(b) What is the median?
1700 1900 1900 2000 2200 2500 19000
Median: 2000
(c) What is the mode?
Mean: 1900
(d) If you compare the results to the results of problem 11, what does this
illustrate?
The average is greatly influenced by the 19000 outlier. The median and mode is not
changed that much by the outlier.
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