Frequency distributions and graphing data: Levels of Measurement Frequency distributions
Chapter 2 CREATING AND USING FREQUENCY DISTRIBUTIONS.
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Transcript of Chapter 2 CREATING AND USING FREQUENCY DISTRIBUTIONS.
Chapter 2
CREATING AND USING FREQUENCY DISTRIBUTIONS
Going Forward
Your goals in this chapter are to learn:• What frequency is and how a frequency
distribution is created• When to graph frequency distributions using a
bar graph, histogram, or polygon• What normal, skewed, and bimodal
distributions are• What relative frequency and percentile are and
how we use the area under the normal curve to compute them
New Symbols and Terminology
• Raw scores are the scores we initially measure in a study
• The number of times a score occurs in a set of data is the score’s frequency
• A frequency distribution organizes the scores based on each score’s frequency
New Symbols and Terminology
• The frequency of a score is symbolized by f• N is the total number of scores in the data
Understanding Frequency Distributions
Frequency Distribution
• A frequency distribution table shows the number of times each score occurs in a set of data
• N is the total of all the individual frequencies in the f column of a frequency distribution table
Raw Scores
Use the following raw scores to construct a frequency distribution table.
14 14 13 15 11 15
13 10 12 13 14 13
14 15 17 14 14 15
Frequency Distribution Table
Graphing Frequency Distributions
• A frequency distribution graph always shows the scores on the X axis and their frequency on the Y axis
• The type of measurement scale (nominal, ordinal, interval, or ratio) determines whether we use– A bar graph– A histogram– A polygon
Frequency Bar Graph for Nominal and Ordinal Data
Histogram for a Small Number of Different Interval or Ratio Scores
Frequency Polygon for Many Different Interval or Ratio Scores
Types of Frequency Distributions
The Normal Distribution
• A bell-shaped curve
• Called a normal curve or a normal distribution
• Symmetrical
• The far left and right portions containing the relatively low-frequency, extreme high or low scores are called the tails of the distribution
An Ideal Normal Distribution
Skewed Distributions
• A skewed distribution is not symmetrical as it has only one pronounced tail
• A distribution may be either negatively skewed or positively skewed
• The direction in which the distinctive tail slopes indicates whether the skew is positive or negative
Negatively Skewed Distribution
A negativelyskewed distribution contains extremelow scores having low frequency, butdoes not contain low-frequency, extreme high scores.
Positively Skewed Distribution
A positivelyskewed distributioncontains extremehigh scores having low frequency, butdoes not contain low-frequency, extreme low scores.
Bimodal Distribution
A bimodaldistribution is asymmetricaldistributioncontaining twodistinct humps.
Frequency Distribution Shape
• The shape of the frequency distribution is an important characteristic of the data
• The shape also determines which statistical procedures we should use
Relative Frequency and the Normal Curve
Relative Frequency
• Relative frequency is the proportion of the time a score occurs in a sample
• The formula for computing a score’s relative frequency is
Relative frequency =N
f
Finding Relative Frequency Using the Normal Curve
The proportion of the total area under the normal curve occupied by a group of scores corresponds to the relative frequency of those scores.
Understanding Percentile and Cumulative Frequency
Percentile
• A percentile is the percent of all scores in the data located below a score
• One way to determine a score’s percentile is to find the area under the normal curve to the left of the score
Cumulative Frequency
The cumulative frequency is the number of
scores in the data that are at or below a
particular score.
Percentiles
Normal distribution showing the area under the curve to the left of selected scores.
Example
Using the following data set, find the relative frequency and cumulative frequency of the score 12.
14 14 13 15 11 15
13 10 12 13 14 13
14 15 17 14 14 15
Example
The frequency table for this set of data.
Example—Relative Frequency
• The frequency for the score of 12 is 1 and N = 18
• Therefore, the relative frequency of 12 is
06.018
1
N
fRelative Frequency
Example—Cumulative Frequency
• There is one score at 12 and two scores below 12 (one score of 11 and one score of 10)
• Therefore, the cumulative frequency of 12 is 3