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30 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Frequency distribution
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When working with large data sets, it is often helpful to organize and summarize data by constructing a table.
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Frequency Distribution
(or Frequency Table) |
shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number (frequency) of data valuesin each of them.
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Lower Class Limits
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are the smallest numbers that can actually belong to different classes
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Upper Class Limits
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are the largest numbers that can actually belong to different classes
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Class Boundaries
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are the numbers used to separate classes, but without the gaps created by class limits.
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Class Midpoints
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are the values in the middle of the classes and can be found by adding the lower class limit to the upper class limit and dividing the sum by 2.
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Class Width
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is the difference between two consecutive lower class limits or two consecutive lower class boundaries
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Reasons for Constructing Frequency Distributions
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1. Large data sets can be summarized.
2. We can analyze the nature of data. 3. We have a basis for constructing importantgraphs. |
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Constructing A Frequency Distribution step 1
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Determine the number of classes (should be between 5 and 20)
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Constructing A Frequency Distribution step 2 |
Calculate the class width (round up).
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Constructing A Frequency Distribution 3 (Starting point)
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Choose the minimum data value or a convenient value below it as the first lower class limit
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Constructing A Frequency Distribution 4 |
Using the first lower class limit and class width, proceed to list the other lower class limits. |
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Constructing A Frequency Distribution 5 |
List the lower class limits in a vertical column and proceed to enter the upper class limits. |
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Constructing A Frequency Distribution 6 |
Take each individual data value and put a tally mark in the appropriate class. Add the tally marks to get the frequency. |
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Class Width
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is the difference between two consecutive lower class limits or two consecutive lower class boundaries
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Reasons for Constructing Frequency Distributions
Step 1 |
Large data sets can be summarized.
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Reasons for Constructing Frequency Distributions
Step 2 |
We can analyze the nature of data.
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Reasons for Constructing Frequency Distributions
Step 3 |
We have a basis for constructing important graphs.
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Relative Frequency Distribution
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Includes the same class limits as a frequency distribution, but the frequency of a classis replaced with a relative frequencies (a proportion) or a percentage frequency ( a percent)
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relative frequency =
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class frequency
sum of all frequencies |
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percentage frequency=
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class frequency
sum of all frequencies x 100 |
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Relative Frequency Distribution
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Cumulative Frequency Distribution
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Critical Thinking: Using Frequency Distributions to UnderstandData 1
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The frequencies start low, then increase to one or two high frequencies, and then decrease to a low frequency.
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Critical Thinking: Using Frequency Distributions to Understand Data 2
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The distribution is approximately symmetric, with frequencies preceding the maximum being roughly a mirror image of those that follow the maximum.
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Gaps
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The presence of gaps can show that we have data from two or more differentpopulations.
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Gaps 2
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However, the converse is not true, because data from different populations do not necessarily result in gaps.
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Example
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Thetable on the next slide is a frequency distribution of randomly selected pennies.
The weights of pennies (grams) are presented, and examination of the frequencies suggests we have two different populations |
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Example 2 |
Pennies made before 1983 are 95% copper and 5% zinc.
Pennies made after 1983 are 2.5% copper and 97.5% zinc. |
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Example (continued)
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