14 Questions
What is the value range of the correlation coefficient?
+1 to -1
What is denoted by 'r' in correlation analysis?
Correlation coefficient
How is the Spearman’s coefficient of rank correlation computed?
Rank the data, calculate the differences in ranks for each variable, square the differences, sum the squared differences, and use the formula to calculate the coefficient.
What does the percentage of non-defective washers produced by the machine represent?
76.98%
What is the percentage of non-defective items produced by a machine?
76.98%
The correlation coefficient can have a value greater than 1.
False
What type of distribution is characterized as a continuous distribution?
Continuous distribution
What is the main purpose of a scatter diagram?
To visualize the relationship between two variables
The mean deviation about mode is usually calculated.
False
The Spearman's rank correlation coefficient is used when the ______________ are not given.
ranks
What is the name of the distribution that is used to model the number of mistakes per day?
Poisson's distribution
Match the following correlation methods with their descriptions:
Scatter Diagram = A visual representation of the relationship between two variables Karl Pearson's Coefficient of Correlation = A quantitative measure of the strength of the linear relationship between two variables Rank Correlation Method = Used for ordinal data when ranks are given Covariance = A measure of the linear relationship between two variables
The area under the normal curve represents the ___________ number of observations.
total
Match the following types of data:
Univariate data = Data that has a single variable or characteristic Bivariate data = Data that has two variables or characteristics Multivariate data = Data that has three or more variables or characteristics
Study Notes
Univariate, Bivariate, and Multivariate Data
- Univariate data: involves one variable
- Bivariate data: involves two variables
- Multivariate data: involves three or more variables
Measures of Central Tendency
- Median: a measure of central tendency, example: median is 36
- Mode: a measure of central tendency, not often used as it is ill-defined
Measures of Dispersion
- Range: a measure of dispersion
- Quartile Deviation (Semi Inter-quartile Range): a measure of dispersion
- Mean Deviation or Average Deviation:
- about Mean
- about Median
- Mean Deviation for Continuous Series: a measure of dispersion
Skewness and Kurtosis
- Skewness: a measure of asymmetry of a distribution
- Kurtosis: a measure of peakedness of a distribution
Probability Distributions
- Binomial Distribution: a discrete probability distribution
- Poisson's Distribution: a discrete probability distribution
- Normal Distribution: a continuous probability distribution
- also known as continuous distribution
- variables can take all values in a given interval
- total area represents total number of observations
Normal Distribution
- Area under the Normal Curve: used to find probability
- Example: finding the percentage of defective washers produced by a machine, assuming the diameters are normally distributed
Correlation Analysis
- Correlation Coefficient (r): a quantitative measure of strength in the linear relationship between two variables
- value lies between +1 to -1
- Methods of finding correlation:
- Scatter Diagram
- Karl Pearson's Coefficient of Correlation
- Rank Correlation Method
- Coefficient of Correlation: a measure of strength and direction of linear relationship between two variables
Spearman's Rank Correlation Coefficient
- used when ranks are given
- example: computing the Spearman's coefficient of rank correlation between academic achievement and family income
Univariate, Bivariate, and Multivariate Data
- Univariate data: involves one variable
- Bivariate data: involves two variables
- Multivariate data: involves three or more variables
Measures of Central Tendency
- Median: a measure of central tendency, example: median is 36
- Mode: a measure of central tendency, not often used as it is ill-defined
Measures of Dispersion
- Range: a measure of dispersion
- Quartile Deviation (Semi Inter-quartile Range): a measure of dispersion
- Mean Deviation or Average Deviation:
- about Mean
- about Median
- Mean Deviation for Continuous Series: a measure of dispersion
Skewness and Kurtosis
- Skewness: a measure of asymmetry of a distribution
- Kurtosis: a measure of peakedness of a distribution
Probability Distributions
- Binomial Distribution: a discrete probability distribution
- Poisson's Distribution: a discrete probability distribution
- Normal Distribution: a continuous probability distribution
- also known as continuous distribution
- variables can take all values in a given interval
- total area represents total number of observations
Normal Distribution
- Area under the Normal Curve: used to find probability
- Example: finding the percentage of defective washers produced by a machine, assuming the diameters are normally distributed
Correlation Analysis
- Correlation Coefficient (r): a quantitative measure of strength in the linear relationship between two variables
- value lies between +1 to -1
- Methods of finding correlation:
- Scatter Diagram
- Karl Pearson's Coefficient of Correlation
- Rank Correlation Method
- Coefficient of Correlation: a measure of strength and direction of linear relationship between two variables
Spearman's Rank Correlation Coefficient
- used when ranks are given
- example: computing the Spearman's coefficient of rank correlation between academic achievement and family income
This quiz covers the concepts of univariate, bivariate, and multivariate data in Business Statistics, including measures of central tendency and dispersion.
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