Kerala PSC Statistical Assistant Exam-Part3
Kerala PSC Statistical Assistant Exam-Part3, Let’s dive into the basics then questins and answers.
Descriptive Statistics
Descriptive statistics is a branch of statistics that focuses on summarizing and describing the features of a data set.
It provides simple summaries about the sample and the measures. These summaries can be either quantitative (numerical) or visual (graphs and charts). Descriptive statistics is divided into several key areas:
Central Tendency
Central tendency measures are used to determine the center of a data set. The most common measures of central tendency are:
- Mean: The average of all data points.
- Median: The middle value when the data points are arranged in ascending order.
- Mode: The most frequently occurring value in the data set.
Dispersion
Dispersion measures are used to describe the spread or variability of the data. Common measures of dispersion include:
- Range: The difference between the highest and lowest values.
- Variance: The average of the squared differences from the mean.
- Standard Deviation: The square root of the variance, indicating how much the data points deviate from the mean.
- Interquartile Range (IQR): The range between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.
Skewness
Skewness measures the asymmetry of the data distribution. It indicates whether the data is skewed to the left (negative skewness) or to the right (positive skewness).
Kurtosis
Kurtosis measures the “tailedness” of the data distribution. It indicates whether the data has heavy tails (leptokurtic), light tails (platykurtic), or normal tails (mesokurtic).
Least Squares
The least squares method is used in regression analysis to minimize the sum of the squared residuals (the differences between observed and predicted values). It helps in finding the best-fitting line for the data.
Correlation
Correlation measures the strength and direction of the linear relationship between two variables. The correlation coefficient ranges from -1 to 1, where:
- 1 indicates a perfect positive correlation.
- -1 indicates a perfect negative correlation.
- 0 indicates no correlation.
Regression
Regression analysis is used to determine the relationship between two or more variables. It helps in predicting the value of a dependent variable based on the value of one or more independent variables.
Multiple Correlation
Multiple correlation measures the strength and direction of the linear relationship between multiple variables. It is used when there are more than two variables involved in the analysis.
Kerala PSC Statistical Assistant Exam-Part3
Central Tendency
- What is the mean of the data set {2, 4, 6, 8, 10}?
- A) 4
- B) 5
- C) 6
- D) 7
- Answer: C) 6
- Which measure of central tendency is most affected by extreme values?
- A) Mean
- B) Median
- C) Mode
- D) None of the above
- Answer: A) Mean
- What is the median of the data set {3, 5, 7, 9, 11}?
- A) 5
- B) 7
- C) 9
- D) 11
- Answer: B) 7
- Which measure of central tendency is the most appropriate for categorical data?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: C) Mode
Dispersion
- What is the range of the data set {15, 22, 8, 19, 31}?
- A) 13
- B) 23
- C) 19
- D) 31
- Answer: B) 23
- Which measure of dispersion is calculated as the square root of the variance?
- A) Range
- B) Mean Deviation
- C) Standard Deviation
- D) Interquartile Range
- Answer: C) Standard Deviation
- What is the variance of the data set {4, 8, 12, 16, 20}?
- A) 16
- B) 20
- C) 24
- D) 25
- Answer: D) 25
- Which measure of dispersion is not affected by extreme values?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Interquartile Range
- Answer: D) Interquartile Range
Skewness
- What does a positive skewness indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: C) Right-skewed distribution
- Which measure is used to determine the skewness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a high kurtosis value indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Symmetrical distribution
- D) Uniform distribution
- Answer: B) Peaked distribution
- Which measure is used to determine the kurtosis of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the purpose of the least squares method in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of 0 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) No correlation
- D) Strong correlation
- Answer: C) No correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
Central Tendency
- What is the mode of the data set {2, 3, 3, 5, 7}?
- A) 2
- B) 3
- C) 5
- D) 7
- Answer: B) 3
- Which measure of central tendency divides the data set into two equal parts?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: B) Median
Dispersion
- What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9}?
- A) 2
- B) 4
- C) 6
- D) 8
- Answer: B) 4
- Which measure of dispersion is the difference between the highest and lowest values in a data set?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Interquartile Range
- Answer: A) Range
Skewness
- What does a negative skewness indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: B) Left-skewed distribution
- Which measure is used to determine the direction of skewness in a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a low kurtosis value indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Symmetrical distribution
- D) Uniform distribution
- Answer: A) Flat distribution
- Which measure is used to determine the peakedness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the least squares method used for in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of 1 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) No correlation
- D) Strong correlation
- Answer: A) Perfect positive correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
Central Tendency
- What is the mean of the data set {10, 20, 30, 40, 50}?
- A) 20
- B) 30
- C) 40
- D) 50
- Answer: B) 30
- Which measure of central tendency is the middle value when the data is arranged in ascending order?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: B) Median
Dispersion
- What is the standard deviation of the data set {2, 4, 6, 8, 10}?
- A) 2.5
- B) 3.0
- C) 3.5
- D) 4.0
- Answer: A) 2.5
- Which measure of dispersion is the average of the squared differences from the mean?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Interquartile Range
- Answer: C) Variance
Skewness
- What does a skewness coefficient of 0 indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: A) Symmetrical distribution
- Which measure is used to determine the asymmetry of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a kurtosis value of 3 indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Mesokurtic distribution
- D) Uniform distribution
- Answer: C) Mesokurtic distribution
- Which measure is used to determine the tailedness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the least squares method used for in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of -1 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) No correlation
- D) Strong correlation
- Answer: B) Perfect negative correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
Central Tendency
- What is the mean of the data set {5, 10, 15, 20, 25}?
- A) 10
- B) 15
- C) 20
- D) 25
- Answer: B) 15
- Which measure of central tendency is the most appropriate for ordinal data?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: B) Median
Dispersion
- What is the range of the data set {12, 18, 24, 30, 36}?
- A) 18
- B) 24
- C) 30
- D) 36
- Answer: B) 24
- Which measure of dispersion is the average of the absolute deviations from the mean?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Mean Absolute Deviation
- Answer: D) Mean Absolute Deviation
Skewness
- What does a skewness coefficient of -1 indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: B) Left-skewed distribution
- Which measure is used to determine the asymmetry of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a kurtosis value greater than 3 indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Mesokurtic distribution
- D) Uniform distribution
- Answer: B) Peaked distribution
- Which measure is used to determine the tailedness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the least squares method used for in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of 0.5 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) Moderate positive correlation
- D) No correlation
- Answer: C) Moderate positive correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
- What is the mean of the data set {7, 14, 21, 28, 35}?
- A) 14
- B) 21
- C) 28
- D) 35
- Answer: B) 21
- Which measure of central tendency is the most appropriate for interval data?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: A) Mean
Dispersion
- What is the standard deviation of the data set {3, 6, 9, 12, 15}?
- A) 3.5
- B) 4.0
- C) 4.5
- D) 5.0
- Answer: B) 4.0
- Which measure of dispersion is the average of the squared differences from the mean?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Interquartile Range
- Answer: C) Variance
Skewness
- What does a skewness coefficient of 1 indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: C) Right-skewed distribution
- Which measure is used to determine the asymmetry of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a kurtosis value less than 3 indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Mesokurtic distribution
- D) Uniform distribution
- Answer: A) Flat distribution
- Which measure is used to determine the tailedness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the least squares method used for in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of -0.5 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) Moderate negative correlation
- D) No correlation
- Answer: C) Moderate negative correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
Central Tendency
- What is the mean of the data set {8, 16, 24, 32, 40}?
- A) 16
- B) 24
- C) 32
- D) 40
- Answer: B) 24
- Which measure of central tendency is the most appropriate for nominal data?
- A) Mean
- B) Median
- C) Mode
- D) Range
- Answer: C) Mode
Dispersion
- What is the range of the data set {5, 10, 15, 20, 25}?
- A) 10
- B) 15
- C) 20
- D) 25
- Answer: B) 20
- Which measure of dispersion is the average of the absolute deviations from the mean?
- A) Range
- B) Standard Deviation
- C) Variance
- D) Mean Absolute Deviation
- Answer: D) Mean Absolute Deviation
Skewness
- What does a skewness coefficient of 2 indicate about the distribution of data?
- A) Symmetrical distribution
- B) Left-skewed distribution
- C) Right-skewed distribution
- D) Uniform distribution
- Answer: C) Right-skewed distribution
- Which measure is used to determine the asymmetry of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Skewness coefficient
- Answer: D) Skewness coefficient
Kurtosis
- What does a kurtosis value greater than 3 indicate about the distribution of data?
- A) Flat distribution
- B) Peaked distribution
- C) Mesokurtic distribution
- D) Uniform distribution
- Answer: B) Peaked distribution
- Which measure is used to determine the tailedness of a data set?
- A) Mean
- B) Median
- C) Mode
- D) Kurtosis coefficient
- Answer: D) Kurtosis coefficient
Least Squares
- What is the least squares method used for in regression analysis?
- A) To minimize the sum of squared residuals
- B) To maximize the sum of squared residuals
- C) To minimize the sum of absolute residuals
- D) To maximize the sum of absolute residuals
- Answer: A) To minimize the sum of squared residuals
- Which of the following is a key assumption of the least squares method?
- A) Homoscedasticity
- B) Heteroscedasticity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Homoscedasticity
Correlation
- What does a correlation coefficient of -0.75 indicate?
- A) Perfect positive correlation
- B) Perfect negative correlation
- C) Strong negative correlation
- D) No correlation
- Answer: C) Strong negative correlation
- Which measure is used to determine the strength and direction of a linear relationship between two variables?
- A) Mean
- B) Median
- C) Correlation coefficient
- D) Standard deviation
- Answer: C) Correlation coefficient
Regression
- What is the purpose of regression analysis?
- A) To determine the relationship between two variables
- B) To determine the central tendency of a data set
- C) To determine the dispersion of a data set
- D) To determine the skewness of a data set
- Answer: A) To determine the relationship between two variables
- Which of the following is a key assumption of linear regression?
- A) Linearity
- B) Non-linearity
- C) Multicollinearity
- D) Autocorrelation
- Answer: A) Linearity
Multiple Correlation
- What does multiple correlation measure?
- A) The relationship between two variables
- B) The relationship between three or more variables
- C) The central tendency of a data set
- D) The dispersion of a data set
- Answer: B) The relationship between three or more variables
- Which measure is used to determine the strength and direction of a linear relationship between multiple variables?
- A) Mean
- B) Median
- C) Multiple correlation coefficient
- D) Standard deviation
- Answer: C) Multiple correlation coefficient
Hope this introduction helps you understand the basics of Descriptive Statistics! If you have any specific questions or need further details, feel free to ask.
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