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Questions and Answers
Which graph type is likely used to represent the percentage distribution of notified TB cases according to type?
Which graph type is likely used to represent the percentage distribution of notified TB cases according to type?
What is the median of the following scores: 19, 16, 2, 10, 15, 5, 17?
What is the median of the following scores: 19, 16, 2, 10, 15, 5, 17?
Which statement about the median is true?
Which statement about the median is true?
What type of distribution has only one mode?
What type of distribution has only one mode?
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Which distribution is characterized by having two modes?
Which distribution is characterized by having two modes?
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When is it appropriate to use the mode as a measure of central tendency?
When is it appropriate to use the mode as a measure of central tendency?
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What is the mode of the scores in Section A: 25, 24, 24, 20, 20, 20, 16, 12, 10, 7?
What is the mode of the scores in Section A: 25, 24, 24, 20, 20, 20, 16, 12, 10, 7?
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Which of the following is NOT a characteristic of the mode?
Which of the following is NOT a characteristic of the mode?
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What is the median score of this set: 2, 5, 10, 15, 16, 17, 19?
What is the median score of this set: 2, 5, 10, 15, 16, 17, 19?
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What is the mean grade ($ar{x}$) calculated from the provided data?
What is the mean grade ($ar{x}$) calculated from the provided data?
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Which subject has the highest individual contribution to the total score ($f(x_i)$)?
Which subject has the highest individual contribution to the total score ($f(x_i)$)?
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What does the median represent in a data distribution?
What does the median represent in a data distribution?
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When is it most appropriate to use the mean as a measure of central tendency?
When is it most appropriate to use the mean as a measure of central tendency?
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If the number of scores (n) is an odd number, how is the median determined?
If the number of scores (n) is an odd number, how is the median determined?
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Which of the following statements about the mean is NOT true?
Which of the following statements about the mean is NOT true?
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What is the total number of units ($ ext{∑f}$) represented in the data?
What is the total number of units ($ ext{∑f}$) represented in the data?
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How many subjects received a grade of 1.00?
How many subjects received a grade of 1.00?
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What is the formula for calculating the range of a set of data?
What is the formula for calculating the range of a set of data?
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Which measure of variability is less influenced by extreme values?
Which measure of variability is less influenced by extreme values?
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How is the mean absolute deviation (M.A.D.) calculated?
How is the mean absolute deviation (M.A.D.) calculated?
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What does a z-score of -2 indicate about a data point?
What does a z-score of -2 indicate about a data point?
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Which equation represents the population standard deviation?
Which equation represents the population standard deviation?
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What is the primary purpose of calculating the variance of a data set?
What is the primary purpose of calculating the variance of a data set?
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What does the coefficient of variation measure?
What does the coefficient of variation measure?
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What is the relationship between sample standard deviation and sample variance?
What is the relationship between sample standard deviation and sample variance?
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What is the primary function of quartiles in data analysis?
What is the primary function of quartiles in data analysis?
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How many equal parts do deciles divide ranked data into?
How many equal parts do deciles divide ranked data into?
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Which measure is used to describe how scores are distributed around a central point?
Which measure is used to describe how scores are distributed around a central point?
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Which of the following represents the correct way to calculate the first quartile from the data set 20, 22, 23, 25, 30, 32, 36?
Which of the following represents the correct way to calculate the first quartile from the data set 20, 22, 23, 25, 30, 32, 36?
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What distinguishes percentiles from quartiles and deciles?
What distinguishes percentiles from quartiles and deciles?
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What happens when the population variability is small?
What happens when the population variability is small?
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Which measure of position is NOT one of the common measures mentioned?
Which measure of position is NOT one of the common measures mentioned?
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In the context of variability, what is indicated by a large variability?
In the context of variability, what is indicated by a large variability?
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What does a z-score of 0 indicate about a student's score?
What does a z-score of 0 indicate about a student's score?
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In comparing the two tests, which statement is true based on z-scores?
In comparing the two tests, which statement is true based on z-scores?
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What is the z-score for a test score of 38 if the mean is 40 and the standard deviation is 5?
What is the z-score for a test score of 38 if the mean is 40 and the standard deviation is 5?
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How is the coefficient of variation (CV) expressed?
How is the coefficient of variation (CV) expressed?
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What does a skewness coefficient (Sk) of less than 0 indicate?
What does a skewness coefficient (Sk) of less than 0 indicate?
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Which type of kurtosis describes a distribution that is flat and spread out?
Which type of kurtosis describes a distribution that is flat and spread out?
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When calculating a z-score, which formula is used?
When calculating a z-score, which formula is used?
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Which of the following is NOT a method of data presentation?
Which of the following is NOT a method of data presentation?
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Study Notes
Descriptive Statistics Overview
- Descriptive statistics summarize and present data, making analysis and interpretation easier
- It involves methods for summarizing and presenting data
Learning Objectives
- Participants will be able to determine methods for summarizing data using descriptive statistics
- Explain the purpose of descriptive statistics and its role in summarizing data
- Define and perform calculations of descriptive statistics
- Interpret and communicate insights derived from descriptive statistics in real-world data contexts
The Domain of Statistics
- Descriptive statistics summarize and present data; inferential statistics draws conclusions about a population based on a sample
Components of Descriptive Statistics
- Data Summarization
- Measures of central tendency (mean, median, mode)
- Measures of location (quartiles, deciles, percentiles)
- Measures of variability (range, interquartile range, mean absolute deviation, variance, standard deviation, z-scores, coefficient of variation)
- Data Presentation
- Narratives
- Tabular presentations
- Graphical presentations (bar graphs, line graphs, pie charts)
Measures of Central Tendency
- A measure of central tendency gives a typical value or representative value of a data set
- It offers a convenient way to represent the performance of a group with one number
- Mean: The arithmetic average of a data set
- Formula: Σxi / N or Σfxi / Σf
- Median: The middle score in a data set (ordered from lowest to highest); 50% below/above median
- Mode: The most frequent value in a data set
- Mean: The arithmetic average of a data set
Measures of Central Location
- It describes where a specific data value falls within a data set, or its relative position compared to other values
- Common measures of position include quartiles, deciles, and percentiles
Quartiles
- Divides the data into four equal parts: Q1, Q2 (Median), Q3
Deciles
- Divides the data into ten equal parts: D1, D2, …, D9
Percentiles
- Divides the data into 100 equal parts: P1, P2, …, P99
Measures of Variability
- Describes the spread or dispersion of data
- Often accompanies measures of central tendency in descriptive statistics
Common Measures of Variability
- Range: Difference between highest and lowest values
- Interquartile Range: Difference between Q3 and Q1
- Mean Absolute Deviation
- Variance & Standard Deviation
- Z-scores
- Coefficient of Variation
Z-Score
- Used to measure relative position of a data point
- Represents standard deviations above or below the mean
- Calculate z-score: (x – mean) / standard deviation
Coefficient of Variation
- Ratio of the standard deviation to the mean, expressed as a percentage
- Measures relative dispersion
Measures of Shape
- Skewness: Absence of symmetry or extreme values on one side of the distribution
- Negatively skewed (left tail is longer)
- Symmetric (no skewedness)
- Positively skewed (right tail is longer)
- Kurtosis: Peakedness of a distribution
- Leptokurtic: High and thin
- Mesokurtic: Normally shaped
- Platykurtic: Flat and spread out
- These measure the overall form/distribution of a data set
Data Presentation Examples
- One-way tables (summarizing data for one variable)
- Cross-tabulations (show the relationship between two or more variables)
- Graphs include bar graphs, line graphs, pie charts
Credits
- CHED seminar facilitators
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Description
This quiz covers the fundamental concepts of descriptive statistics, focusing on methods for summarizing and presenting data. Participants will explore measures of central tendency, variability, and how to interpret data insights effectively. By the end, learners will understand the significance of descriptive statistics in real-world applications.
