Frequency Tables Frequency Distributions Conclusion MATH 105: Finite Mathematics 9-3: Organizing Data Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006
Frequency Tables Frequency Distributions Conclusion Outline Frequency Tables 1 Frequency Distributions 2 Conclusion 3
Frequency Tables Frequency Distributions Conclusion Outline Frequency Tables 1 Frequency Distributions 2 Conclusion 3
Frequency Tables Frequency Distributions Conclusion A Large Data Set A typical larger data set may contain a wide range of data values and even have repeated values. It is often difficult to work with this raw data. Example The following is a list of scores made on a 60-point test. 25 30 34 37 41 42 46 49 53 26 31 34 37 41 42 46 50 53 28 31 35 37 41 43 47 51 54 29 32 36 38 41 44 48 52 54 30 33 36 39 41 44 48 52 55 30 33 37 40 42 45 48 52 Construct a frequency table for this data.
Frequency Tables Frequency Distributions Conclusion A Large Data Set A typical larger data set may contain a wide range of data values and even have repeated values. It is often difficult to work with this raw data. Example The following is a list of scores made on a 60-point test. 25 30 34 37 41 42 46 49 53 26 31 34 37 41 42 46 50 53 28 31 35 37 41 43 47 51 54 29 32 36 38 41 44 48 52 54 30 33 36 39 41 44 48 52 55 30 33 37 40 42 45 48 52 Construct a frequency table for this data.
Frequency Tables Frequency Distributions Conclusion Frequency Table Example Below is a frequency table for the data shown previously. Value Freq. Value Freq. Value Freq. 25 1 36 2 46 2 26 1 37 4 47 1 28 1 38 1 48 3 29 1 39 1 49 1 30 3 40 1 50 1 31 2 41 5 51 1 32 1 42 3 52 3 33 2 43 1 53 2 34 2 44 2 54 2 35 1 45 1 55 1
Frequency Tables Frequency Distributions Conclusion Line Chart A frequency table can be represented graphically using a line chart.
Frequency Tables Frequency Distributions Conclusion Outline Frequency Tables 1 Frequency Distributions 2 Conclusion 3
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Grouping The Data Frequency tables are helpful, but they still leave the data too spread out in some cases. And, as you can see from the previous example, there is still a lot of data to keep track of. To help remedy that, we group the data together. Frequency Distribution A frequency distribution counts the number of data points in equal-sized ranges, called class intervals. Creating a Frequency Distribution To create a frequency distribution: 1 Find the range of the data (largest value - smallest value) 2 Find the class width (range / # classes) 3 Find the class intervals (repeatedly adding class width) 4 Count the data in each interval
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Lower Class Limits: The first number in the range. Upper Class Limits: The second number in the range. Class Midpoint upper − lower 2
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 Lower Class Limits: 31-33.99 5 The first number in the range. 34-36.99 5 Upper Class Limits: 37-39.99 6 The second number in the range. 40-42.99 9 43-45.99 4 Class Midpoint 46-48.99 6 49-51.99 3 upper − lower 52-55 7 2
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 Lower Class Limits: 31-33.99 5 The first number in the range. 34-36.99 5 Upper Class Limits: 37-39.99 6 The second number in the range. 40-42.99 9 43-45.99 4 Class Midpoint 46-48.99 6 49-51.99 3 upper − lower 52-55 7 2
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 Lower Class Limits: 31-33.99 5 The first number in the range. 34-36.99 5 Upper Class Limits: 37-39.99 6 The second number in the range. 40-42.99 9 43-45.99 4 Class Midpoint 46-48.99 6 49-51.99 3 upper − lower 52-55 7 2
Frequency Tables Frequency Distributions Conclusion Now, we create a frequency distribution using the test score data seen earlier. Example Construct a frequency distribution using 10 class intervals. Class Interval Frequency 25-27.99 2 28-30.99 5 Lower Class Limits: 31-33.99 5 The first number in the range. 34-36.99 5 Upper Class Limits: 37-39.99 6 The second number in the range. 40-42.99 9 43-45.99 4 Class Midpoint 46-48.99 6 49-51.99 3 upper − lower 52-55 7 2
Frequency Tables Frequency Distributions Conclusion A Histogram The bar chart which is used with a frequency distribution is called a histogram. The line is called a frequency polynomial.
Frequency Tables Frequency Distributions Conclusion Another Frequency Distribution What happens if we use the same data with a different number of classes? Example Construct a frequency distribution using a class width of 5. Question: Does changing the class width change the shape of the histogram?
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