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Published byEdmund Kelly Modified over 5 years ago

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What is a frequency distribution? A table that shows classes (intervals) of data entries with a count of the number of entries in each class Frequency (f) – the number of data entries in the class

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How do you create a frequency distribution? 1. Choose how many classes (you will be given this information) 2. Calculate class width: highest entry – lowest entry # of classes 3. Find each class’s lower and upper limits 4. Sort entries into classes (tallies) 5. Count tallies to find f for each class

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Example 1 The following sample data lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a frequency distribution that has seven classes. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44

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Example 1 (cont’d) 1. Number of classes is given to you (7) 2. Class width: 88 – 7 = 11.57 ≈ 12 7 3. Since the lower limit of the first class will be 7, the lower limit of the second class will be 7+12 = 19, and so on.

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Example 1 - Frequency Distribution ClassTallyf 7-18 19-30 31-42 43-54 55-66 67-78 79-90 Σf=50 6 10 13 8 5 6 2

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What else can be done in a frequency distribution? Midpoint=lower class limit+upper class limit 2 Relative Frequency: portion of the data set is in a class RF = class frequency = f sample sizen Cumulative Frequency: sum of the frequency for that class plus all previous classes

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Example 2 Using the frequency distribution constructed for Example 1, find the midpoint, relative frequency, and cumulative frequency for each class.

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Example 2(cont’d) Class f Mdpt RelFreqCumFreq 7-18 6 19-30 10 31-42 13 43-54 8 55-66 5 67-78 6 79-90 2 Σf = 50 12.5 24.5 36.5 48.5 60.5 72.5 84.5.12.2.26.16.1.12.04 Σf/n = 1.00 6 16 29 37 42 48 50

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HOMEWORK Worksheet 2-1 #3, 4, 5, 6, 15, 16

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What is a frequency histogram? Bar graph showing the frequency distribution of a data set Horizontal scale (x-axis) is quantitative and measures data values Vertical scale (y-axis) measures frequency of classes Bars MUST touch each other (no gaps) Use MIDPOINTS as x-values Bars should be drawn to straddle each midpoint line

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Example 3 Draw a frequency histogram for the frequency distribution in Example 2. Time online (minutes) Frequency (# of subscribers) 12.5 24.5 36.5 48.5 60.5 72.5 84.5 2 4 6 8 10 12 14

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What is a frequency polygon? Line graph to show CHANGE in frequencies USES MIDPOINTS as x-values

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Example 4 Draw a frequency polygon for the frequency distribution in Example 2. Time online (minutes) Frequency (# of subscribers) 12.5 24.5 36.5 48.5 60.5 72.5 84.5 96.5 2 4 6 8 10 12 14

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HOMEWORK Worksheet 2-1 #17, 18, 29, 30

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What is a relative frequency histogram? Same as a frequency histogram, but shows RELATIVE frequencies Use UPPER CLASS BOUNDARIES as x-values Have one more decimal place than the data Eliminates any gaps between classes Example: If the class LIMITS are 10-15, the class BOUNDARIES will be 9.5 to 15.5 Use relative frequencies as y-values Bars should be drawn to span from the lower class boundary to upper class boundary (between vertical lines, not straddling the lines)

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Example 5 Draw a relative frequency histogram for the frequency distribution in Example 2. Time online (minutes) Relative Frequency (Portion of subscribers) 6.5 18.5 30.5 42.5 54.5 66.5 78.5 90.5.04.08.12.16.2.24.28

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What is an ogive? Also known as cumulative frequency graph Line graph Use UPPER CLASS BOUNDARIES as x-values Use cumulative frequencies as y-values Points are placed on the upper class boundary lines

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Example 6 Draw an ogive for the frequency distribution in Example 2. Estimate how many subscribers spent less than 60 minutes during their last session. Time online (minutes) Cumulative Frequency (# of subscribers) 6.5 18.5 30.5 42.5 54.5 66.5 78.5 90.5 10 20 30 40 50

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In conclusion… How do you create a frequency distribution? Draw a quick sketch of each: Frequency histogram Frequency polygon Relative frequency histogram Ogive

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HOMEWORK Worksheet 2-1 #21, 22, 25, 26

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