ECO 391 Exam 1 | Actual study set |
Questions and verified Answers
4 Measures of Central Location - ANSW-1. Mean
2. Median
3. Mode
4. Weighted Mean
4 Measures of Variability - ANSW-1. Range
2. Variance
3. Standard Deviation
4. Coefficient of Variation
2 Measures of Association - ANSW-1. Covariance
2. Correlation Coefficient
Mean - ANSW-- The mean of a data set is the average of all the data values
- The sample mean (x̄) is the point estimator of the population mean (μ)
- The mean might not reflect the sample/population because it is susceptible to outliers
Sample Mean - ANSW-Formula: x̄ = (Σxi / n)
Σxi = sum of the values of the n observations
n = number of observations in the sample
Population Mean - ANSW-Formula: μ = (Σxi / N)
Σxi = sum of the values of the N observations
N = number of observations in the population
Median - ANSW-- The median of a data set is the value in the middle when the data items are arranged
in ascending order.
- Whenever a data set has extreme values, the median is the preferred measure of central location.
- Equals 50th Percentile
- When there's an even number of observations average the two values
Mode - ANSW-- The mode is the most frequently occurring value in a data set
- The greatest frequency can occur at two or more different values
- A data can have no mode, one mode (unimodal), or many modes (multimodal)
The Weighted Mean - ANSW-- The weighted mean is relevant when some observations contribute more
than others
- Formula (for a sample): x̄ = Σwixi
The Range - ANSW-- The range of a data set is the difference between the largest and smallest data
values
- Range = Largest Value - Smallest Value
The Variance - ANSW-- The variance is the average of the squared differences between each data value
and the mean
, - Used to calculate standard deviation
Variance (for a population) - ANSW-Formula: σ² = (Σ(xi-μ)²) / N
Variance (for a sample) - ANSW-Formula: s² = (Σ(xi-x̄ )²) / (n-1)
Standard Deviation - ANSW-- The standard deviation of a data set is the positive square root of the
variance
- It tells us how measurements for a group are spread out from mean or the expected value
Standard Deviation (for a population) - ANSW-Formula: σ = √(σ²)
Standard Deviation (for a sample) - ANSW-Formula: s = √(s²)
The Coefficient of Variation - ANSW-The coefficient of variation indicates how large standard deviation is
in relation to the mean
Coefficient of Variation (for a population) - ANSW-Formula: [(σ/μ) x 100]%
Coefficient of Variation (for a sample) - ANSW-Formula: [(s/x̄ ) x 100]%
The Covariance - ANSW-- The covariance describes the direction of the linear relationship between two
variables, X and Y
- Positive: Upward Sloping, Negative: Downward Sloping
Covariance (for a population) - ANSW-Formula: σxy = (Σ(xi-μx)(yi -μy)) / N
Covariance (for a sample) - ANSW-Formula: sxy = (Σ(xi-x̄ )(yi -ȳ)) / (n-1)
Correlation Coefficient - ANSW-- The correlation coefficient describes BOTH the direction and the
strength of the relationship between two variables, X and Y
- Weak: Dots far from line, Strong: Dots close or on line
Correlation Coefficient (for a population) - ANSW-Formula: ρxy = σxy / (σxσy)
Correlation Coefficient (for a sample) - ANSW-Formula: rxy = sxy / (sxsy)
Central Limit Theorem - ANSW-Does not apply to small sample sizes (the larger, the more approximate
our ANSWer)
Descriptive Statistics - ANSW-- Are brief descriptive coefficients that summarize a given data set, which
can be either a representation of the entire population or the sample
- Can be broken down into measures of central tendency and measures of variability
- Ex. Mode, Median, St. Dev
Inferential Statistics - ANSW-Are used by taking a random sample of data from a population to describe
and make inferences about the population
Population - ANSW-- Consists of all items of interest in a statistical problem
- The Population Parameters are usually unknown
- Parameter: numerical characteristic of a population
Sample - ANSW-- Subset of the population
- The Sample Statistic is calculated from the sample and can be used to make inferences about the
population
Why do we take samples and not survey the whole population? - ANSW-1. Obtaining information on the
entire population is expensive
2. In many cases it is impossible to examine every member of the population
Questions and verified Answers
4 Measures of Central Location - ANSW-1. Mean
2. Median
3. Mode
4. Weighted Mean
4 Measures of Variability - ANSW-1. Range
2. Variance
3. Standard Deviation
4. Coefficient of Variation
2 Measures of Association - ANSW-1. Covariance
2. Correlation Coefficient
Mean - ANSW-- The mean of a data set is the average of all the data values
- The sample mean (x̄) is the point estimator of the population mean (μ)
- The mean might not reflect the sample/population because it is susceptible to outliers
Sample Mean - ANSW-Formula: x̄ = (Σxi / n)
Σxi = sum of the values of the n observations
n = number of observations in the sample
Population Mean - ANSW-Formula: μ = (Σxi / N)
Σxi = sum of the values of the N observations
N = number of observations in the population
Median - ANSW-- The median of a data set is the value in the middle when the data items are arranged
in ascending order.
- Whenever a data set has extreme values, the median is the preferred measure of central location.
- Equals 50th Percentile
- When there's an even number of observations average the two values
Mode - ANSW-- The mode is the most frequently occurring value in a data set
- The greatest frequency can occur at two or more different values
- A data can have no mode, one mode (unimodal), or many modes (multimodal)
The Weighted Mean - ANSW-- The weighted mean is relevant when some observations contribute more
than others
- Formula (for a sample): x̄ = Σwixi
The Range - ANSW-- The range of a data set is the difference between the largest and smallest data
values
- Range = Largest Value - Smallest Value
The Variance - ANSW-- The variance is the average of the squared differences between each data value
and the mean
, - Used to calculate standard deviation
Variance (for a population) - ANSW-Formula: σ² = (Σ(xi-μ)²) / N
Variance (for a sample) - ANSW-Formula: s² = (Σ(xi-x̄ )²) / (n-1)
Standard Deviation - ANSW-- The standard deviation of a data set is the positive square root of the
variance
- It tells us how measurements for a group are spread out from mean or the expected value
Standard Deviation (for a population) - ANSW-Formula: σ = √(σ²)
Standard Deviation (for a sample) - ANSW-Formula: s = √(s²)
The Coefficient of Variation - ANSW-The coefficient of variation indicates how large standard deviation is
in relation to the mean
Coefficient of Variation (for a population) - ANSW-Formula: [(σ/μ) x 100]%
Coefficient of Variation (for a sample) - ANSW-Formula: [(s/x̄ ) x 100]%
The Covariance - ANSW-- The covariance describes the direction of the linear relationship between two
variables, X and Y
- Positive: Upward Sloping, Negative: Downward Sloping
Covariance (for a population) - ANSW-Formula: σxy = (Σ(xi-μx)(yi -μy)) / N
Covariance (for a sample) - ANSW-Formula: sxy = (Σ(xi-x̄ )(yi -ȳ)) / (n-1)
Correlation Coefficient - ANSW-- The correlation coefficient describes BOTH the direction and the
strength of the relationship between two variables, X and Y
- Weak: Dots far from line, Strong: Dots close or on line
Correlation Coefficient (for a population) - ANSW-Formula: ρxy = σxy / (σxσy)
Correlation Coefficient (for a sample) - ANSW-Formula: rxy = sxy / (sxsy)
Central Limit Theorem - ANSW-Does not apply to small sample sizes (the larger, the more approximate
our ANSWer)
Descriptive Statistics - ANSW-- Are brief descriptive coefficients that summarize a given data set, which
can be either a representation of the entire population or the sample
- Can be broken down into measures of central tendency and measures of variability
- Ex. Mode, Median, St. Dev
Inferential Statistics - ANSW-Are used by taking a random sample of data from a population to describe
and make inferences about the population
Population - ANSW-- Consists of all items of interest in a statistical problem
- The Population Parameters are usually unknown
- Parameter: numerical characteristic of a population
Sample - ANSW-- Subset of the population
- The Sample Statistic is calculated from the sample and can be used to make inferences about the
population
Why do we take samples and not survey the whole population? - ANSW-1. Obtaining information on the
entire population is expensive
2. In many cases it is impossible to examine every member of the population
