1.1 Terminology Flashcards
Does a sample mean the same thing in statistics and biology?
No, for example, sample and population are not the same in statistics and in biology
What is an individual observation?
Value (numerical or not) taken by a variable observed on an individual
What is the smallest unit in data collection? What are other units?
- Individual (smallest)
- Group
- Population (largest)
What is a statistical sample of size n? What is it also called?
- n individual observations
- Also called “sample data”
- n values taken by a variable observed on n individuals
For a given variable, how many individual observations would be observed for 1 individual?
1 individual observation
For a given variable, how many individual observations would be observed for a group of n individuals? What is this called?
n individual observations (statistical sample)
For a given variable, how many individual observations would be observed for a population of N individuals? What is this called?
N individual observations (statistical population)
What is the difference between n and N?
- N>= n
- n (statistical sample)
- N (statistical population)
What are the two main types of random variables?
- Qualitative (characters)
- Quantitative (numbers: integers, fractions, or real numbers)
What is the nominal scale?
- All one can do with the observations is “name” them
- Ex: symbols (+, -, $)
What is the ordinal scale?
- There is an order to allow for observations to be ranked: alphabetical or numerical
What is the interval scale?
- In the absence of a true zero point, data can be positive or negative
- Or, are strictly positive, so that ratios make sense
- Ex: temperatures in celsius, IQ
What is a ratio scale?
- There is a true zero point and ratios do make sense
- Ex: temperatures in Kelvin
“Plant vigor, from weak to strong” is an example of what kind of scale?
Ordinal
“Temperature in celsius” is an example of what kind of scale?
Interval
”+, -, $, ?” is an example of what kind of scale?
Nominal
“Temperature in Kelvin” is an example of what kind of scale?
Ratio
What is a random variable?
Associated with the uncertainty of the outcome of an observation
List the scales of observation from the scale that you can manipulate the least to the most.
- Nominal (least)
- Ordinal
- Interval
- Ratio (most)
What are three orders used by the ordinal scale?
- Alphabetical (A is smaller than B)
- Numerical
- Grades (A is greater than B)
“Numerical codes, such as 032, 134, etc.” are an example of which kind of scale?
Ordinal scale
Which scales of observation are qualitative? Which scales are quantitative?
- Qualitative: nominal and ordinal
- Quantitative: interval and ratio
Define an individual.
Location observed on a given day at a given time
Can the length of an interval be negative?
No, it must always be positive
Statistically speaking, the number of towns visited by a candidate on a day during an election campaign (Note: Candidates may take ‘days off’, when they visit no town.) is observed at the _________ scale.
ratio
Statistically speaking, the number of towns visited by a candidate on a day during an election campaign represents what kind of data?
Discrete quantitative
Statistically speaking, the budget of a government in a given year (defined as the sum of predicted incomes and outcomes, rounded to the nearest million of the national currency) is observed at the _________ scale.
interval
Statistically speaking, the budget of a government in a given year (defined as the sum of predicted incomes and outcomes, rounded to the nearest million of the national currency) represents what kind of data?
Discrete quantitative
True or False: The sample mean is random because its value changes from random sample to random sample.
True
True or False: The variance of a random sample made of negative numbers is zero or positive.
True
True or False: The expected value of the sum of two random variables is always equal to the sum of the population
means of the two random variables.
True
True or False: In the general case, the population variance of the sum of two random variables is equal to the sum of the population variances of the two random variables plus an extra term.
True
True or False: The “3M statistics” are not all equal when the sample distribution is symmetrical and bimodal.
True
True or False: A sample variance is negative.
False
True or False: The sample mean and the sample standard deviation are expressed in the same unit.
True
True or False: The “3M statistics” are not all equal when the sample distribution is skewed.
True
True or False: By definition, the coefficient of variation is a percentage.
True
The magnitude of an earthquake, rounded to the first decimal, is observed (statistically speaking) at the _____ scale.
interval
The magnitude of an earthquake, rounded to the first decimal is what type of variable?
Discrete quantitative
When traveling around the world, there usually is a time delay between the clock times in the departure city and once at destination, called “jet lag”, which is a number of hours: 0, 1, 2, 3, … 14 between Montréal and Tokyo. The jet lag, depending on the travel/traveler, is observed (statistically speaking) at the _________ scale.
ratio
Jet lag, a number of hours, is what type of variable?
Discrete quantitative
True or False: The variance of a sample made of constant quantities (e.g., n = 3 and x1 = x2 = x3 = 10) is zero.
True
True or False: By definition, the sample mean
is non-negative.
False
The destination (city, country) of a holiday trip is an example of what kind of data?
Qualitative
The difference between the number of passengers on a “go flight” from destination A to destination B in a given evening and the number of passengers on the “return flight” from destination B to destination A in the following morning is an example of what kind of variable? The random variable is observed at the _________ scale.
Discrete quantitative
interval
True or False: The median may exist for a sample of qualitative data.
True
True or False: The population mean of a normal distribution is also its population median and population mode
True
True or False: The sample mean and the sample variance are expressed in the same unit.
False
True or False: The population variance is zero.
True
The exact distance (without rounding to the nearest km) between the departure point and the arrival point is an example of what variable?
Continuous quantitative
The consumption of meat per Canadian resident (expressed in kg, without any rounding) is an example of what variable?
Continuous quantitiative
The distribution of the world human population per continent (expressed as a percentage, rounded to the nearest percent) is an example of what variable?
Discrete quantitative
The diet regime of an animal (e.g. herbivorous, carnivorous, omnivorous) is an example of what variable?
Qualitative
The date on which a mine accident occurs in the world is an example of a random variable observed at which scale of observation?
Ordinal scale
In a survey made by a company, the level of satisfaction of an employee at work, expressed as “highly satisfied”, “moderately satisfied”, “moderately unsatisfied”, and “excessively unsatisfied” is an example of which variable? Which scale of observation does it utilize?
- Qualitative
- Ordinal scale
The budget of a company, expressed as the difference between incomes and outcomes in a given year, is an example of which variable? Which scale of observation does it utilize?
- Discrete quantitative
- Interval scale
The number of people who hold a valid car driving license in a family is an example of which variable?
Discrete quantitative
The balance of the budget of a government (i.e. incomes minus expenses) can be seen as a random variable observed (statistically) at which scale of observation?
Interval scale
The colour of a leaf on a maple at the end of October (i.e. from yellow to brown, with green, orange and red in-between) is an example of which variable? Which scale of observation does it utilize?
- Qualitative
- Ordinal
True or False: The “3M statistics” are all equal, while the sample distribution is symmetrical and has one mode.
True
True or False: The “3M statistics” are all equal, while the sample distribution is symmetrical and has two modes.
False
True or False: The sample mean and the sample variance are expressed in different units.
True
True or False: The population variance is negative.
False
