BBS_Chpt2

2. Tally the data 3. Find the numerical frequencies from the tallies 4. Find the cumulative frequencies (depends on type of graph)
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Constructing Grouped Frequency Distribution
Example 2-2:
Step 1: Determine the classes. Find the highest and lowest value: H= 134 and L=100 Find the range: R = highest value –lowest value= H – L R = 134 – 100 = 34
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3 Types of Frequency Distributions
• A categorical frequency distribution is used when the data is at nominal or ordinal level. Eg:
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A grouped frequency distribution is used when the range is large and classes of several units in width are needed. Eg:
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• The class midpoint is found by adding the lower and upper boundaries (or limits) and dividing by 2. Eg.(100+104)÷2 =102 or (99.5+104.5 )÷2 =102
Constructing Grouped Frequency Distribution
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Class Boundaries, Class Width and Class Midpoint
• Class boundaries have one additional place value and end in a 5. Eg. • The class width for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class from the the lower (or upper) class limit of the next class. Eg. 105-100=5 or 109-104=5
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Constructing Grouped Frequency Distribution
Find upper class limits: Subtract one unit from the lower class limit of second class to get upper limit of the first class. Then add class width to each upper limit to get all the upper limits. So, 105-1 =104; 104 + 5 = 109; 109 + 5 = 114, etc. Find the class boundaries: Subtract 0.5 from each lower class limit and add 0.5 to each upper class limit. So, class boundaries for the first class are, 100- 0.5=99.5 and 104+0.5 = 104.5
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The Role of Graphs
• The purpose of graphs in statistics is to convey the data to the viewer in pictorial form. • Graphs are useful in getting the audience’s attention in a publication or a presentation.
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Rules for Constructing Classes
• There should be between 5 and 20 classes. • The class width should preferably be an odd number. • The classes must be mutually exclusive. • The classes must be continuous. • The classes must be exhaustive. • The classes must be equal width. Except when there is an open-ended distribution.
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Grouped Frequency Distributions
• The lower class limit represents the smallest data value that can be included in the class. • The upper class limit represents the largest value that can be included in the class. • The class boundaries are used to separate the classes so that there are no gaps in the frequency distribution.
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Histograms, Frequency Polygons and Ogives
• The histogram displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.
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Constructing Grouped Frequency Distribution
Step 2: Tally the data. Step 3: Find the numerical frequencies from the tallies. Step 4: Find the cumulative frequencies . Add frequency in each class to the total of the frequencies of the classes preceding that class. So, 0+2 = 2, 2+8=10, 10+18=28, 28+13=41, etc. The completed frequency distribution is:
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Histograms, Frequency Polygons and Ogives
• The frequency polygon displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes.
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Histograms, Frequency Polygons and Ogives
• The cumulative frequency or ogive represents the cumulative frequencies for the classቤተ መጻሕፍቲ ባይዱs in a frequency distribution.
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Constructing Grouped Frequency Distribution
Select the number of classes desired: In this example, we choose 7 classes as stated in question. Find the class width: Class Width = R / number of classes = 34 / 7 = 4.9 Rounding up gives Class width as 5. Select a starting point and find lower class limits: The starting point can be the smallest data value or any convenient number less than the smallest data value. In this example, 100 is used. Add class width to 100 to get the lower class limit for the next class. Keep adding until there are 7 classes, that is, 100, 105, 110, etc.
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3 Types of Frequency Distributions
When the range of data is small, a frequency distribution can be constructed using single data values for each class. This type of distribution is called an ungrouped frequency distribution.