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Questions and Answers
A ________ table is often used to display data when the data have a very large range of values.
A ________ table is often used to display data when the data have a very large range of values.
grouped frequency
A grouped frequency table is likely to have between 5 and ________ classes.
A grouped frequency table is likely to have between 5 and ________ classes.
15
If a grouped frequency table has five classes with the first class 1 - 13, what should be the lower limit of the third class?
If a grouped frequency table has five classes with the first class 1 - 13, what should be the lower limit of the third class?
27
What is the midpoint of the lowest class in a grouped frequency table of placement test scores shown above?
What is the midpoint of the lowest class in a grouped frequency table of placement test scores shown above?
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The relative frequency of the second class is ______%.
The relative frequency of the second class is ______%.
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The cumulative frequency of the last class is ____.
The cumulative frequency of the last class is ____.
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What does a histogram display?
What does a histogram display?
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What does a bar chart display?
What does a bar chart display?
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Calculate the mean of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
Calculate the mean of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
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Calculate the median of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
Calculate the median of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
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Calculate the mode of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
Calculate the mode of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
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What do your answers to the previous three questions tell you about the distribution?
What do your answers to the previous three questions tell you about the distribution?
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If ten students scored 45, 62, 63, 58, 81, 77, 64, 69, 82, 51, what percentile does the score of 69 represent?
If ten students scored 45, 62, 63, 58, 81, 77, 64, 69, 82, 51, what percentile does the score of 69 represent?
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What is Q2 (the median) for the given placement test scores?
What is Q2 (the median) for the given placement test scores?
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What were the scores of the students who scored above the third quartile?
What were the scores of the students who scored above the third quartile?
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Calculate the sum of squares of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
Calculate the sum of squares of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.
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Calculate the sample variance of the above data set.
Calculate the sample variance of the above data set.
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Calculate the sample standard deviation of the above data set.
Calculate the sample standard deviation of the above data set.
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What are raw data points?
What are raw data points?
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What do researchers use to organize and display values observed?
What do researchers use to organize and display values observed?
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Which of the following is not a type of frequency distribution?
Which of the following is not a type of frequency distribution?
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A ________ is a structured presentation of data that shows discrete data values, or scores, together with the frequency of each score.
A ________ is a structured presentation of data that shows discrete data values, or scores, together with the frequency of each score.
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If 2 out of 3 dentists recommend a certain kind of gum, what percentage of dentists is that, rounded to the nearest whole number?
If 2 out of 3 dentists recommend a certain kind of gum, what percentage of dentists is that, rounded to the nearest whole number?
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A grouped frequency table is most useful when which of the following is true?
A grouped frequency table is most useful when which of the following is true?
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A ________ is a structured presentation of data based on frequencies of classes rather than frequencies of specific values.
A ________ is a structured presentation of data based on frequencies of classes rather than frequencies of specific values.
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How do histograms differ from bar graphs?
How do histograms differ from bar graphs?
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The bars representing data touch each other in a ______.
The bars representing data touch each other in a ______.
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Which of the following accurately describes the axes of a histogram?
Which of the following accurately describes the axes of a histogram?
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In a frequency polygon, the y-axis represents the __________.
In a frequency polygon, the y-axis represents the __________.
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With a frequency polygon, what does grounding the shape mean?
With a frequency polygon, what does grounding the shape mean?
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A positive skew may have a tail that indicates extreme scores __________ the center of the distribution.
A positive skew may have a tail that indicates extreme scores __________ the center of the distribution.
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A negative skew may have a tail that indicates extreme scores __________ the center of the distribution.
A negative skew may have a tail that indicates extreme scores __________ the center of the distribution.
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What type of effect causes positively skewed data due to minimum sales constraints typically faced by school-aged children fundraising?
What type of effect causes positively skewed data due to minimum sales constraints typically faced by school-aged children fundraising?
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What type of effect corresponds to a negatively skewed distribution when most students score exceptionally high?
What type of effect corresponds to a negatively skewed distribution when most students score exceptionally high?
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Numbers that describe samples are called?
Numbers that describe samples are called?
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Numbers that describe populations are called?
Numbers that describe populations are called?
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The mean of the population is represented by the symbol?
The mean of the population is represented by the symbol?
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A bimodal distribution has __________ modes.
A bimodal distribution has __________ modes.
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The most frequently occurring score in a distribution is the?
The most frequently occurring score in a distribution is the?
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Study Notes
Grouped Frequency Tables
- Grouped frequency tables display data with a wide range of values, typically using 5 to 15 classes.
- For a table with five classes, if the first class ranges from 1-13, the lower limit of the third class is 27.
- The midpoint of the lowest class can be calculated as (0+9)/2 = 4.5.
Relative and Cumulative Frequency
- Relative frequency can be calculated as a proportion of the total, for example, 4% from a class frequency of 1 out of 25 total observations.
- The cumulative frequency for the last class in a sample of 25 scores is 25.
Visual Data Representation
- A histogram shows frequencies of numerical data, while a bar chart presents frequencies of categorical data.
- Histograms show continuous data and have touching bars; bar charts display distinct categories with gaps between bars.
- The x-axis of a histogram represents variable values, while the y-axis indicates frequency.
Central Tendency and Distribution
- To find the mean, add all data points and divide by the number of points, yielding a value of approximately 64.13 for the given dataset.
- The median is the middle value when the data is ordered; for the dataset, the median is 73.
- The mode, the most frequently occurring score, is 79.
Distribution Characteristics
- The described dataset is unimodal and negatively skewed, indicated by the relationship between mean, median, and mode.
- Percentiles provide context for performance; a score of 69 corresponds to the 60th percentile in a test of 10 students.
Quartiles and Score Analysis
- Q2, or the median, for a test scoring dataset is 63.5.
- Scores above the third quartile (75th percentile) for the listed test scores are 81 and 82.
Variability Measures
- The sum of squares is a measure of variance, with a value of approximately 11239.733 for the dataset.
- Sample variance is calculated as approximately 802.8381, and the sample standard deviation is around 28.3344.
Data Types and Frequency Distribution
- Raw data points are original, unaltered observations.
- Frequency tables organize data for clearer analysis, contrasting with inferential tables which do not exist as a type of frequency distribution.
- Grouped frequency tables summarize data frequencies over continuous value ranges.
Distribution Skewness and Effects
- A positive skew has a tail of extreme scores above the center of the distribution, while a negative skew has a tail below it.
- "Floor effects" occur when minimum thresholds skew data positively due to constraints, while "ceiling effects" correspond to negatively skewed data when scores cluster near a ceiling.
Statistical Concepts
- Sample descriptions are referred to as statistics, and population descriptions are known as parameters.
- The symbol "μ" represents the mean of a population.
- A bimodal distribution features two distinct modes, or peaks, in frequency.
Studying That Suits You
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Description
Test your knowledge with these flashcards covering key concepts from Statistics 230, Chapter 2. This quiz focuses on grouped frequency tables and their usage in displaying data. Enhance your understanding of how to interpret and create these tables effectively.
