1. Frequency Distributions and Percentiles
Chapter Three
Frequency Distributions and Percentiles

2. New Statistical Notation
The number of times a score occurs is the score’s frequency, which is symbolized by f
A distribution is the general name for any organized set of data
N is the sample size indicating the number of scores
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3. Simple Frequency Distributions
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4. Simple Frequency Distribution
A simple frequency distribution shows the number of times each score occurs in a set of data
The symbol for a score’s simple frequency is simply f
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5. Raw Scores
Following is a data set of raw scores. We will use these raw scores to construct a simple frequency distribution table. 14 13 15 11 10 12 17
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6. Simple Frequency Distribution Table
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7. Graphing a Simple Frequency Distribution
A frequency distribution graph 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
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8. A Simple Frequency Bar Graph Is Used for Nominal and Ordinal Data.
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9. A Histogram Is Used for a Small Range of Different Interval or Ratio Scores.
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10. A Frequency Polygon Is Used for a Large Range of Different Scores
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11. Types of Simple Frequency Distributions
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12. The Normal Distribution
A bell-shaped curve
Called the normal curve or a normal distribution
It is symmetrical
The far left and right portions containing the low-frequency extreme scores are called the tails of the distribution
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13. An Ideal Normal Distribution
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14. A distribution may be either negatively skewed or positively skewed
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
Whether a skewed distribution is negative or positive corresponds to whether the distinct tail slopes toward or away from zero
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15. Negatively Skewed Distribution
A negatively skewed distribution contains extreme low scores that have a low frequency, but does not contain low frequency extreme high scores
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16. Positively Skewed Distribution
A positively skewed distribution contains extreme high scores that have a low frequency, but does not contain low frequency extreme low scores
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17. Bimodal Distribution
A bimodal distribution is a symmetrical distribution containing two distinct humps
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18. Rectangular Distribution
A rectangular distribution is a symmetrical distribution shaped like a rectangle
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19. Relative Frequency and the Normal Curve
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20. Relative frequency is the proportion of time the score occurs
The symbol for relative frequency is rel. f
The formula for a score’s relative frequency is
rel. f =
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21. A Relative Frequency Distribution
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22. Finding Relative Frequency Using the Normal Curve
The proportion of the total area under the normal curve that is occupied by a group of scores corresponds to the combined relative frequency of those scores.
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23. Computing Cumulative Frequency and Percentile
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24. Cumulative Frequency
Cumulative frequency is the frequency of all scores at or below a particular score
The symbol for cumulative frequency is cf
To compute a score’s cumulative frequency, we add the simple frequencies for all scores below the score with the frequency for the score
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25. A Cumulative Frequency Distribution
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26. Percentile
A percentile is the percent of all scores in the data that are at or below the score
If the scores cumulative frequency is known, the formula for finding the percentile is
Score’s Percentile =
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27. Finding Percentiles
The percentile for a given score corresponds to the percent of the total area under the curve that is to the left of the score.
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28. Percentiles Normal distribution showing the area under the
curve to the left of selected scores.
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29. Grouped Frequency Distributions
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30. Grouped Distributions
In a grouped distribution, scores are combined to form small groups, and then we report the total f, rel. f, or cf of each group
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31. A Grouped Distribution
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32. Example 1
Using the following data set, find the relative frequency of the score 12 14 13 15 11 10 12 17
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33. The simple frequency table for this set of data is as follows.
Example 1
The simple frequency table for this set of data is as follows.
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34. The frequency for the score of 12 is 1. N = 18.
Example 1
The frequency for the score of 12 is 1. N = 18.
Therefore, the rel. f of 12 is
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35. Example 2 What is the cumulative frequency for the score of 14?
Answer: The cumulative frequency of 14 is the frequency of all scores at or below 14 in this data set
cf = = 13
The cf for the score of 14 in this data set is 13
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36. Example 3 What is the percentile for the score of 14?
Answer: The percentile of 14 is the percentage of all scores at or below 14 in this data set
= 0.72
Another way to calculate this percentile is
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