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3-2 example3

# 3-2 example3 - Student Grady Simonton Course Math119...

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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:17 ANI Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the (a) mean, (b) median, (0) mode, and (d) midrange for the given sample data in millions of dollars. Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general? Are such top 10 lists valuable for gaining insight into the larger population? 40.4 36.3 34.3 26.1 141312 9.6 9.5 7.2 a. The mean of a set of values is the measure of center found by adding the values and dividing the total by the number of values. x (- sum of all data values mean = n (— number of data values To calculate the mean, ﬁrst calculate the sum of the data values. Zx = 40.4 +36.8 +34.3 +26.1 +14 +13 +12 +9.6 +9.5 +7.2 = 202.9 Then divide the sum by the number of data values to get the mean, ;. The number of values is 10. Z X n x: 202.9 10 20.29 Thus, the mean is 20.29 million dollars. I). The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude. If there is an even number of data values, the median is the mean of the two middle data values. Arrange the data in order of increasing magnitude. 7.2 9.5 9.6 12 l3 14 26.] 34.3 36.3 40.4 Since the number of data values is even, the median is found by computing the mean of the two middle numbers, 13 and 14. First, add the two middle numbers. 13 + 14 = 27 To find the median, divide the sum of the two middle numbers by 2. 27 Median = 7 = 13.5 Page 1 Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:17 ANI Thus, the median is 13.5 million dollars. c. The mode of a data set is the value that occurs with the greatest frequency. If two or more data values occur with the same greatest frequency, then there are multiple modes. If no data value is repeated, it can be said that there is no mode. Since there is no value with a frequency greater than 1, the values have no mode. d. The midrange of a data set is the measure of center that is the value midway between the maximum and minimum values in the original data set. It is found by adding the maximum data value to the minimum data value and then dividing the sum by 2, as shown in the formula below. maximum value + minimum value 2 midrange = Find the maximum and minimum values of the data set in millions of dollars. The maximum value is 40.4 and the minimum value is 7.2. Add the two values and divide the sum by 2. _ 40.4 + ”:22 midrange = T = 23.8 Therefore, the midrange is 23.8 million dollars. The top 10 salaries give information about the top salaries of TV personalities. In order to have information about the salaries of TV personalities in general, the sample values have to represent such group. Top 10 lists are valuable for gaining insight into a certain segment of the population, however, they provide no information about the larger population. Page 2 ...
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3-2 example3 - Student Grady Simonton Course Math119...

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