chapter 2 notes - STA 2023 Elementary Statistics Lecture...

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STA 2023 Elementary Statistics Lecture Notes Chapter 2 – Descriptive Statistics Professor Achenbach Frequency Distributions A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that are in each class. This number is called the frequency of the class. Example: Statistics exam grades. Suppose that 20 statistics students’ scores on an exam are as follows: 97, 92, 88, 75, 83, 67, 89, 55, 72, 78, 81, 91, 57, 63, 67, 74, 87, 84, 98, 46 We can construct a frequency table with classes 90-99, 80-89, 70-79 etc. by counting the number of grades in each grade range. Class Frequency ( f ) 90-99 4 80-89 6 70-79 4 60-69 3 50-59 2 40-49 1 Note that the sum of the frequency column is equal to 20, the number of test scores. 1
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Additional Terminology Lower Class Limit – The least value that can belong to a class. Upper Class Limit – The greatest value that can belong to a class. Class Width – The difference between the upper (or lower) class limits of consecutive classes. All classes should have the same class width. Class Midpoint – The middle value of each data class. To find the class midpoint, average the upper and lower class limits. upper lower class midpoint = 2 + Example: From the frequency table of statistics grades above. The upper class limits are 99, 89, 79, 69, 59, and 49. The lower class limits are 90, 80, 70, 60, 50, and 40. The class midpoints are 94.5, 84.5, 74.5, 64.5, 54.5, and 44.5. The width of each class is 10. Creating a Frequency Table 1. Decide on the number of data classes you wish to use. 2. Divide the range of the data ( 29 range highest value lowest value = - by the number of classes to get an estimate of class width. 3. Decide on class bounds 4. Construct the frequency table by counting the number of data values in each class Class Exercise: Construct a frequency table with 6 data classes from the following data set. (p. 44 # 27) Amount of gasoline purchased by 28 drivers: 7, 4, 18, 4, 9, 8, 8, 7, 6, 2, 9, 5, 9, 12, 4, 14, 15, 7, 10, 2, 3, 11, 4, 4, 9, 12, 5, 3 2
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In this course, the following symbols and variables will have the meanings given below. (unless otherwise specified) Variables x = data value n = number of values in a sample data set N = number of values in a population data set f = frequency of a data class Symbol indicates the sum of all values for the following variable or expression. Example: Using our notation, we can write the statement that the sum of the frequencies in a frequency table should equal the number of values in the data set as follows: f n = Cumulative Frequency The cumulative frequency of a data class is the number of data elements in that class and all previous classes. (can be done ascending or descending) Example: Class Frequency ( f ) Cumulative Frequency 90-99 4 4 80-89 6 10 70-79 4 14 60-69 3 17 50-59 2 19 40-49 1 20 Notice that the last entry in the cumulative frequency column is
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chapter 2 notes - STA 2023 Elementary Statistics Lecture...

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