Topic 1 Flashcards
What are statistics?
The methods that help transform data into useful information for decision makers.
Define descriptive statistics.
They refer to methods that primarily help summarize and present data.
Define inferential statistics.
They refer to methods that use data collected from a small group to reach conclusions about a larger group.
What is a population?
The collection of things under consideration.
What is a sample?
A portion of the population selected for analysis.
What is a parameter?
A summary measure computed to describe a characteristic of the population.
What is a statistic?
A summary measure computed to describe a characteristic of the sample.
What is a variable?
A characteristic of an item or individual.
What is data?
- the information we gather about the sample or the population
- the different values associated with the variable
- the information to be analysed
What are the two classification types of data?
- Categorical Data
- Numerical data
Data can also be classified based on its level of measurement.
These are:
- Nominal
- Ordinal
- Interval
- Ratio
Why is it important to know the classification distinctions of data?
- Nominal
- Ordinal
- Interval
- Ratio
Because the type of data often governs the choice of methodology used in subsequent analysis.
What is meant by the property of central tendency?
- the extent to which the data values are grouped around a central value
- a number that represents the ‘middle’ of the sample data
- a value around which the observations ‘cluster’
What is the sample mean?
The sum of the values in a sample divided by the number of values in the sample.
Advantage:
It is the only measure in which all the values play an equal role.
What is the median?
The middle value in an ordered array of data that has been ranked from smallest to largest.
Half the values are smaller or equal than the median and half the values are larger of equal to the median value.
Advantage:
It is not affected by extreme values, so it can be used when extreme values are present.
What is the mode?
The value in a set that appears most frequently.
Advantage:
The mode is the only average that can be used if the data set is not in numbers, for instance the colours of cars in a car park.
What does variation measure?
The spread and dispersion of values in a data set.
Define range.
The difference between the largest and smallest value.
Define sample variance.
An average of the squared differences in a data set from their sample mean.
(the sum of squares divided by the sample size minus 1)
What is the sample standard deviation?
An average deviation.
The square root of the sample variance.
What does the Z-score measure?
The position of a particular observation from the mean.
It is measured in a “standardized” value, Z.
The magnitude of the Z- score tells us how many sample standard deviations the observation is away from the sample mean.
What is the Empirical rule?
For a sufficiently large data set that has a bell-shaped distribution:
- Approximately 68% of observations in a data set lie within one sample standard deviation of the sample mean.
- Approximately 95% of observations in a data set lie within two sample standard deviations of the sample mean.
- Virtually all observations (99.7%) in a data set lie within three sample standard deviations of the sample mean.
What are the properties of a set of numerical data?
Numerical data properties measure:
- central tendency
- variation
- relative standing
What are the differences between the measures of variation?
Variation measures the spread and dispersion of values in a data set:
- range is the difference between the largest and smallest value
- sample variance is an average of the squared differences in a data set from their sample mean
- the sample standard deviation is an average deviation
What is an interval scale?
A numerical variable that expresses a difference between measurements that do not include a true zero point, e.g. temperature in degrees Celsius.
What is a ratio scale?
A numerical variable of an ordered scale that includes a true zero point, e.g. the cost of an object.
What is a nominal scale?
A categorical variable that expresses no order or ranking.
For example, a law subject, a business subject, a statistics subject.
What is an ordinal scale?
A categorical variable where an ordering or ranking of category values is implied.
Ordinal scales give you some information to compare values but not as much as interval or ratio scales.
For example, pass, credit, distinction, high distinction.
The methods involving the collection, presentation of data in tables, figures and graphs, and characterization of a set of data in order to properly describe the various features of that set of data are called:
A) the scientific method.
B) statistical inference.
C) sampling.
D) descriptive statistics.
The methods involving the collection, presentation of data in tables, figures and graphs, and characterization of a set of data in order to properly describe the various features of that set of data are called:
A) the scientific method.
B) statistical inference.
C) sampling.
D) descriptive statistics.
The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of:
A) a statistic.
B) a parameter.
C) inferential statistics.
D) descriptive statistics.
The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of:
A) a statistic.
B) a parameter.
C) inferential statistics.
D) descriptive statistics.
A summary measure that is computed to describe a characteristic from only a sample of the population is called:
A) a statistic.
B) the scientific method.
C) a census.
D) a parameter.
A summary measure that is computed to describe a characteristic from only a sample of the population is called:
A) a statistic.
B) the scientific method.
C) a census.
D) a parameter.
Which of the following is most likely a population as opposed to a sample?
A) every third person to arrive at the bank.
B) registered voters in a county.
C) respondents to a newspaper survey.
D) the first 5 students completing an assignment.
Which of the following is most likely a population as opposed to a sample?
A) every third person to arrive at the bank.
B) registered voters in a county.
C) respondents to a newspaper survey.
D) the first 5 students completing an assignment.
The study of the collection, analysis, summarization, organization and interpretation of data is known as:
A) Economics
B) Mathematics
C) Statistics
D) None of the above
The study of the collection, analysis, summarization, organization and interpretation of data is known as:
A) Economics
B) Mathematics
C) Statistics
D) None of the above
Which of the following is most likely a parameter as opposed to a statistic?
A) The proportion of trucks stopped yesterday that were cited for bad brakes.
B) The average height of people randomly selected from a database.
C) The average score of the first five students completing an assignment.
D) The proportion of females registered to vote in a county.
Which of the following is most likely a parameter as opposed to a statistic?
A) The proportion of trucks stopped yesterday that were cited for bad brakes.
B) The average height of people randomly selected from a database.
C) The average score of the first five students completing an assignment.
D) The proportion of females registered to vote in a county.
Which of the following statistics is not a measure of central tendency?
A) median
B) Q3
C) mode
D) arithmetic mean
Which of the following statistics is not a measure of central tendency?
A) median
B) Q3
C) mode
D) arithmetic mean
In a perfectly symmetrical bell-shaped ʺnormalʺ distribution:
A) the median equals the mode.
B) the arithmetic mean equals the median.
C) the arithmetic mean equals the mode.
D) All of the above.
In a perfectly symmetrical bell-shaped ʺnormalʺ distribution:
A) the median equals the mode.
B) the arithmetic mean equals the median.
C) the arithmetic mean equals the mode.
D) All of the above.
The smaller the spread of scores around the arithmetic mean,
A) the smaller the interquartile range.
B) the smaller the coefficient of variation.
C) the smaller the standard deviation.
D) All of the above.
The smaller the spread of scores around the arithmetic mean,
A) the smaller the interquartile range.
B) the smaller the coefficient of variation.
C) the smaller the standard deviation.
D) All of the above.
According to the empirical rule, if the data form a ʺbell-shapedʺ normal distribution, _____ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.
A) 68
B) 95
C) 93.75
D) 9.99
According to the empirical rule, if the data form a ʺbell-shapedʺ normal distribution, _____ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.
A) 68
B) 95
C) 93.75
D) 9.99
The method involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data is called:
(a) scientific method
(b) statistical inference
(c) descriptive statistics
(d) none of the above
The method involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data is called:
(a) scientific method
(b) statistical inference
(c) descriptive statistics
(d) none of the above
The universe or “totality of items or things” under consideration is called:
(a) a sample
(b) a statistic
(c) a population
(d) a parameter.
The universe or “totality of items or things” under consideration is called:
(a) a sample
(b) a statistic
(c) a population
(d) a parameter.
The portion of the universe that has been selected for analysis is called:
(a) a sample
(b) a statistic
(c) a population
(d) a parameter.
The portion of the universe that has been selected for analysis is called:
(a) a sample
(b) a statistic
(c) a population
(d) a parameter.
A summary measure that is computed to describe a characteristic of an entire population is called:
(a) a census
(b) a statistic
(c) a parameter
(d) the scientific method.
A summary measure that is computed to describe a characteristic of an entire population is called:
(a) a census
(b) a statistic
(c) a parameter
(d) the scientific method.
A summary measure that is computed to describe a characteristic from only a sample of the population is called:
(a) a census
(b) a statistic
(c) the scientific method
(d) a parameter.
A summary measure that is computed to describe a characteristic from only a sample of the population is called:
(a) a census
(b) a statistic
(c) the scientific method
(d) a parameter.
