Stats Chapter 2: Frequency Distributions

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Questions and Answers

What is the definition of frequency distribution?

A frequency distribution is an organized tabulation of the number of individuals located in each category on the scale of measurement.

What are the two elements presented in a frequency distribution?

List of all individual scores

Graphical representation of data

Categories of measurement scale (correct)

Frequency of individuals in each category (correct)

What do proportion measures represent?

The fraction of the total group that is associated with each score.

What is the formula for proportion?

Proportion = frequency over n Signup and view all the answers

What is the definition of relative frequency?

The proportion of the total distribution rather than the absolute frequency. Signup and view all the answers

Do proportions more commonly appear as fractions?

False Signup and view all the answers

What is the formula to calculate percentage?

p times 100, or 100 times the frequency over n Signup and view all the answers

What is the definition of 'range' in statistics?

The distance from the upper real limit of the highest score to the lower real limit of the lowest score. Signup and view all the answers

What is a grouped frequency distribution table?

A table that groups scores into intervals instead of listing each individual score. Signup and view all the answers

The groups, or intervals, in a grouped frequency distribution table are called _.

class intervals Signup and view all the answers

What are the guidelines for grouped frequency distribution tables?

<ol> <li>Have about 10 class intervals. 2. Width of each interval should be a relatively simple number. 3. Bottom score in each class interval should be a multiple of the width. 4. All intervals should be the same width.</li> </ol> Signup and view all the answers

What is the purpose of a frequency distribution?

To help researchers see the data. Signup and view all the answers

What is the formula to know how many rows to create in a frequency table?

Higher number minus lowest number plus 1 Signup and view all the answers

What are apparent limits?

The score values that appear as the lowest score and the highest score in an interval. Signup and view all the answers

The horizontal line is the X-axis, or the _________.

abscissa Signup and view all the answers

The vertical line is the Y-axis, or the ______.

ordinate Signup and view all the answers

What is the general rule for graph height in relation to its length?

The height (Y-axis) should be approximately two-thirds to three-quarters of its length (X-axis). Signup and view all the answers

What are the two types of graphs for interval or ratio data?

Histograms or polygons. Signup and view all the answers

How do you construct a histogram?

List numerical scores along the X-axis and draw bars above each X value according to their frequency. Signup and view all the answers

What is a modified histogram?

A variation of the traditional histogram using stacks of blocks representing individuals instead of bars. Signup and view all the answers

How do you construct a polygon?

List numerical scores along the X-axis, place a dot above each score for frequency, and connect the dots with a line. Signup and view all the answers

Study Notes

Frequency Distribution Overview

A frequency distribution organizes and tabulates the number of individuals in each measurement category.
It can be presented as a table or a graph, both capturing the same core elements: the measurement scale categories and their corresponding frequencies.

Proportions and Formulas

Proportion calculates the fraction of the total group represented by each score.
Formula for proportion: proportion = frequency / n.
Relative frequency refers to the proportion of the total distribution, useful when absolute frequencies are unknown.
Proportions are typically expressed in decimals rather than fractions.
Percentage formula: percentage = p × 100 or percentage = 100 × (frequency / n).

Range and Grouped Frequency Distributions

Range is defined as the distance from the highest score's upper limit to the lowest score's lower limit.
A grouped frequency distribution table consolidates scores into intervals, representing ranges (e.g., number of students scoring in the 90s).

Class Intervals in Grouped Frequency Tables

Grouped frequency distribution tables should contain about 10 class intervals for clarity—too many lead to clutter, too few lose data granularity.
Each class interval's width should be a simple number and the bottom score should be a multiple of this width.
Ensure all intervals are of the same width, creating a clear distinction for each score.

Purpose of Frequency Distributions

Frequency distributions aid researchers in visualizing data patterns and frequencies.

Creating Frequency Tables

To determine the number of rows for a frequency table, use the formula: highest number - lowest number + 1.
Apparent limits are the lowest and highest scores that are visible in the intervals.

Graphs and their Construction

The X-axis (abscissa) and Y-axis (ordinate) are standard graph components for depicting frequency distributions.
A good practice is making the graph height about two-thirds to three-quarters of its length.

Types of Graphs for Data

Two types of graphical representations for interval or ratio data include histograms and polygons.

Histograms

Constructing a histogram involves listing numerical scores on the X-axis and drawing a bar corresponding to each frequency.
The height of the bar matches the frequency, and the width extends to the real limits of the category for continuous variables.

Modified Histograms

A modified histogram replaces bars with stacks of blocks, where each block represents an individual and corresponds numerically to frequency.

Polygons

Building a polygon involves placing a dot above each score on the X-axis corresponding to frequency, then connecting the dots with a continuous line.
The graph should extend to the X-axis at both ends, completing the visual representation of the data.

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Description

This quiz covers key concepts from Statistics Chapter 2, focusing on frequency distributions. It includes definitions, structures, and the essential elements involved in creating frequency distributions. Test your knowledge on how these distributions are organized and presented.