Frequency Tables Constructing a Frequency Table for GROUPED DATA From a Set of Data In some cases, we may encounter a dataset which has no repeated datavalues, or may have many different values. In these cases, it is more useful to construct a frequency table where each row in the table represents an interval of data and not just a single data value. To set up a Frequency Table for Grouped Data, we need to determine "classes". Classes are categories into which the data will be grouped. Each class will have a lower class limit and an upper class limit. Let's say we are working with a dataset which records the distance that employees travel one-way to work. We may have a row in the frequency table that shows an interval of 10.0 to 14.9 and we would determine how many workers travel between 10.0 miles and 14.9 miles to work. In this example, 10.0 would be called the lower class limit and 14.9 would be called the upper class limit. In order to set up a frequency table for Grouped Data, we need to determine these class limits for each row in the table. To do this we will calculate what is called the class width. The class width is the difference between consecutive lower class limits (from one row to the next). How To Construct a frequency table for a grouped data set Step 1: Determine the number of rows (or classes) for the Frequency Table. Typically we select the number of rows to be between 5 and 20 . Step 2: Calculate the class width using the formula: Class Width = Max Value − Min Value Number of Classes Step 3: Note: For integer data, round the class width up to the next higher whole number. Step 4: Create a table with the number of rows equal to the number of classes. Create columns for Lower Class Limit, Upper Class Limit, and Frequency. Step 5: Set Lower Class Limit for the 1 st row equal to the minimum value from the data set. Step 6: Calculate the Lower Class Limit for the 2 nd row as the lower class limit from 1 st row plus the class width. Add the class width to calculate the lower class limit for the other rows. Step 7: The Upper Class Limit for each row is one less than the lower class limit from the subsequent row. You can also add the class width to each upper class limit to determine the upper class limit for the subsequent row. Step 8: Frequency for each Row: count of how many datavalues fall between the lower class limit and upper class limit for that row. Example: Frequency Table for Grouped Data The data values given below represent the final exam scores for a statistics class. Construct a frequency table for grouped data using 5 classes. For convenience, the data values have been ordered from smallest to largest. 64 , 69 , 70 , 71 , 73 , 73 , 74 , 76 , 80 , 83 , 85 , 86 , 86 , 91 , 93 , 94 , 95 , 97 , 98 , 100 1. The number of classes has been predetermined for us. We will use 5 classes. 2. Class Width = Max Value − Min Value Number of Classes Class Width = 100 − 64 5 = 7.2 3. Since this is integer data, we round the class width up to the next higher whole number. So, we will use a class width of 8 . 4. Will will now create a table with 5 rows to represent the five class widths. The table will also have 3 columns to hold the values of Lower Class Limit, Upper Class Limit, and Frequency for each class. Lower Class LimitUpper Class LimitFrequency 5. Set Lower Class Limit for the 1 st row equal to the minimum value from the dataset. The minimum data value is 64 . Lower Class LimitUpper Class LimitFrequency 64 6. Calculate the Lower Class Limit for the 2 nd row as the lower class limit from 1 st row plus the class width. Add the class width to calculate lower class limit for other rows. Since the class width is 8 , each lower class will increment by 8. For example, the lower limit of the second class is 64 8 = 72 . The lower class limit for the third class is 72 8 = 80 , etc. Lower Class LimitUpper Class LimitFrequency 64 72 80 88 96 7. The Upper Class Limit for each row is one less than the lower class limit from the subsequent row. You can also add the class width to each upper class limit to determine the upper class limit for the subsequent row. Note that the lower class limit of the second row is 72 , so the upper class limit of the first row would be 72 − 1 = 71 . Also note that the lower class limit of the third row is 80 , so the upper class limit of the second row would be 80 − 1 = 79 . Notice that the upper class limits also increment by 8 , the class width. Lower Class LimitUpper Class LimitFrequency 64 71 72 79 80 87 88 95 96 103 8. Frequency for each Row: count of how many data values fall between the lower class limit and upper class limit for that row. 4 data values are between 64 and 71 . These data values are: 64 , 69 , 70 , and 71 . 4 data values are between 72 and 79 . These data values are: 73 , 73 , 74 , and 76 . We continue counting the frequency for all remaining classes. Lower Class LimitUpper Class LimitFrequency 64 71 4 72 79 4 80 87 5 88 95 4 96 103 3

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drcindydowis drcindydowis

04-05-2024
Mathematics

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Frequency Tables Constructing a Frequency Table for GROUPED DATA From a Set of Data In some cases, we may encounter a dataset which has no repeated datavalues, or may have many different values. In these cases, it is more useful to construct a frequency table where each row in the table represents an interval of data and not just a single data value. To set up a Frequency Table for Grouped Data, we need to determine "classes". Classes are categories into which the data will be grouped. Each class will have a lower class limit and an upper class limit. Let's say we are working with a dataset which records the distance that employees travel one-way to work. We may have a row in the frequency table that shows an interval of 10.0 to 14.9 and we would determine how many workers travel between 10.0 miles and 14.9 miles to work. In this example, 10.0 would be called the lower class limit and 14.9 would be called the upper class limit. In order to set up a frequency table for Grouped Data, we need to determine these class limits for each row in the table. To do this we will calculate what is called the class width. The class width is the difference between consecutive lower class limits (from one row to the next). How To Construct a frequency table for a grouped data set Step 1: Determine the number of rows (or classes) for the Frequency Table. Typically we select the number of rows to be between 5 and 20 . Step 2: Calculate the class width using the formula: Class Width = Max Value − Min Value Number of Classes Step 3: Note: For integer data, round the class width up to the next higher whole number. Step 4: Create a table with the number of rows equal to the number of classes. Create columns for Lower Class Limit, Upper Class Limit, and Frequency. Step 5: Set Lower Class Limit for the 1 st row equal to the minimum value from the data set. Step 6: Calculate the Lower Class Limit for the 2 nd row as the lower class limit from 1 st row plus the class width. Add the class width to calculate the lower class limit for the other rows. Step 7: The Upper Class Limit for each row is one less than the lower class limit from the subsequent row. You can also add the class width to each upper class limit to determine the upper class limit for the subsequent row. Step 8: Frequency for each Row: count of how many datavalues fall between the lower class limit and upper class limit for that row. Example: Frequency Table for Grouped Data The data values given below represent the final exam scores for a statistics class. Construct a frequency table for grouped data using 5 classes. For convenience, the data values have been ordered from smallest to largest. 64 , 69 , 70 , 71 , 73 , 73 , 74 , 76 , 80 , 83 , 85 , 86 , 86 , 91 , 93 , 94 , 95 , 97 , 98 , 100 1. The number of classes has been predetermined for us. We will use 5 classes. 2. Class Width = Max Value − Min Value Number of Classes Class Width = 100 − 64 5 = 7.2 3. Since this is integer data, we round the class width up to the next higher whole number. So, we will use a class width of 8 . 4. Will will now create a table with 5 rows to represent the five class widths. The table will also have 3 columns to hold the values of Lower Class Limit, Upper Class Limit, and Frequency for each class. Lower Class LimitUpper Class LimitFrequency 5. Set Lower Class Limit for the 1 st row equal to the minimum value from the dataset. The minimum data value is 64 . Lower Class LimitUpper Class LimitFrequency 64 6. Calculate the Lower Class Limit for the 2 nd row as the lower class limit from 1 st row plus the class width. Add the class width to calculate lower class limit for other rows. Since the class width is 8 , each lower class will increment by 8. For example, the lower limit of the second class is 64 8 = 72 . The lower class limit for the third class is 72 8 = 80 , etc. Lower Class LimitUpper Class LimitFrequency 64 72 80 88 96 7. The Upper Class Limit for each row is one less than the lower class limit from the subsequent row. You can also add the class width to each upper class limit to determine the upper class limit for the subsequent row. Note that the lower class limit of the second row is 72 , so the upper class limit of the first row would be 72 − 1 = 71 . Also note that the lower class limit of the third row is 80 , so the upper class limit of the second row would be 80 − 1 = 79 . Notice that the upper class limits also increment by 8 , the class width. Lower Class LimitUpper Class LimitFrequency 64 71 72 79 80 87 88 95 96 103 8. Frequency for each Row: count of how many data values fall between the lower class limit and upper class limit for that row. 4 data values are between 64 and 71 . These data values are: 64 , 69 , 70 , and 71 . 4 data values are between 72 and 79 . These data values are: 73 , 73 , 74 , and 76 . We continue counting the frequency for all remaining classes. Lower Class LimitUpper Class LimitFrequency 64 71 4 72 79 4 80 87 5 88 95 4 96 103 3

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