3-2 example4

# 3-2 example4 - Student Grady Si1nonton Course Math119...

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Unformatted text preview: Student: Grady Si1nonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:18 ANI Find the (a) mean, (b) median, (0) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deﬁciency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where l = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4 = wrinkled-green. Do the results make sense? 4 4 2 3 4 4 2 l 2 4 l 4 l 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. 2 x (— sum of all sample values Mean = n (— number of sample values In order to calculate the mean, ﬁrst sum all the values. 2.. 4+4+2+3+4+4+2+1+2+4+1+4+1+2 38 To ﬁnd the mean, divide the sum, 38, by the number of observations. In this problem there are 14 observations. 1.4-2 ea] 14 as 2.7 Thus, the mean phenotype code is 2.7. (b) 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 magnitude. First arrange the data in increasing order of magnitude. 1 1 2 2 2 2 3 4 4 4 4 4 4 If the number of values is odd, the median is the number located in the exact middle of the list. If the number of values is even, the median is found by computing the mean of the two middle numbers. Since there are 14 observations, the number of values is even. Thus, the median is the mean of the two middle observations, 2 and 3. 2+3 2 2.5 Median Page 1 Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 11:18 ANI Thus, the median phenotype code is 2.5. (c) The mode of a data set is the value that occurs most often. To determine the mode, start by determining the ﬁ‘equency of each code. Notice that 1, 2, and 4 all have a frequency greater than one. Determine each of their frequencies. The data set is listed in ascending order on the right. Phenotype Codes 1 l l 2 2 2 2 3 4 4 4 4 4 4 Since 4 has the highest frequency, it is the mode. Thus, the mode of the phenotype codes is 4. (d) The midrange is the measure of center that is the value midway between the maximum and minimum values in the original data set. The midrange is given by the following formula. maximum value + minimum value ‘dra = m1 nge 2 Start by identifying the maximum and minimum values of the data set. The data set is listed in ascending order on the right. The maximum value is 4. Phenotype Codes 1 1 1 2 2 2 2 3 4 4 4 4 4 4 The minimum value is 1. Now calculate the midrange of the data set. 4+1 2 2.5 midrange Thus, the midrange of the phenotype codes is 2.5. Among the different measures of center, mean, median, mode, and midrange, only the mode can be used with data at the nominal level of measurement. Recall that the nominal level of measurement applies to data that consists of names, labels or categories only. The data set is nominal because 1, 2, 3, and 4 represent four different phenotype categories. Page 2 ...
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