Statistics 230 Chapter 2 Flashcards

Questions and Answers

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.

If a grouped frequency table has five classes with the first class 1 - 13, what should be the lower limit of the third class?

What is the midpoint of the lowest class in a grouped frequency table of placement test scores shown above?

4.5 Signup and view all the answers

The relative frequency of the second class is ______%.

4% Signup and view all the answers

The cumulative frequency of the last class is ____.

25 Signup and view all the answers

What does a histogram display?

Frequencies of numerical data Signup and view all the answers

What does a bar chart display?

Frequencies of categories Signup and view all the answers

Calculate the mean of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.

64.13 Signup and view all the answers

Calculate the median of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.

73 Signup and view all the answers

Calculate the mode of the following data set: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79.

79 Signup and view all the answers

What do your answers to the previous three questions tell you about the distribution?

It is unimodal and negatively skewed Signup and view all the answers

If ten students scored 45, 62, 63, 58, 81, 77, 64, 69, 82, 51, what percentile does the score of 69 represent?

60th percentile Signup and view all the answers

What is Q2 (the median) for the given placement test scores?

63.5 Signup and view all the answers

What were the scores of the students who scored above the third quartile?

81, 82 Signup and view all the answers

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.

11239.733 Signup and view all the answers

Calculate the sample variance of the above data set.

802.8381 Signup and view all the answers

Calculate the sample standard deviation of the above data set.

28.3344 Signup and view all the answers

What are raw data points?

Data points in their original form Signup and view all the answers

What do researchers use to organize and display values observed?

Frequency table Signup and view all the answers

Which of the following is not a type of frequency distribution?

Inferential table Signup and view all the answers

A ________ is a structured presentation of data that shows discrete data values, or scores, together with the frequency of each score.

Frequency table Signup and view all the answers

If 2 out of 3 dentists recommend a certain kind of gum, what percentage of dentists is that, rounded to the nearest whole number?

67 Signup and view all the answers

A grouped frequency table is most useful when which of the following is true?

Data vary over a large range of continuous values Signup and view all the answers

A ________ is a structured presentation of data based on frequencies of classes rather than frequencies of specific values.

Grouped frequency table Signup and view all the answers

How do histograms differ from bar graphs?

Histograms are typically used to depict frequencies of continuous data, but bar graphs are typically used to depict categorical data. Signup and view all the answers

The bars representing data touch each other in a ______.

Histogram Signup and view all the answers

Which of the following accurately describes the axes of a histogram?

The x-axis shows the variable values; the y-axis shows frequency Signup and view all the answers

In a frequency polygon, the y-axis represents the __________.

Frequencies Signup and view all the answers

With a frequency polygon, what does grounding the shape mean?

Adding a value on both ends of the axis so lines can be drawn to zero Signup and view all the answers

A positive skew may have a tail that indicates extreme scores __________ the center of the distribution.

Above Signup and view all the answers

A negative skew may have a tail that indicates extreme scores __________ the center of the distribution.

Below Signup and view all the answers

What type of effect causes positively skewed data due to minimum sales constraints typically faced by school-aged children fundraising?

floor Signup and view all the answers

What type of effect corresponds to a negatively skewed distribution when most students score exceptionally high?

ceiling Signup and view all the answers

Numbers that describe samples are called?

Statistics Signup and view all the answers

Numbers that describe populations are called?

Parameters Signup and view all the answers

The mean of the population is represented by the symbol?

mu Signup and view all the answers

A bimodal distribution has __________ modes.

two Signup and view all the answers

The most frequently occurring score in a distribution is the?

mode Signup and view all the answers

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.

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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.