Figure 1 The data are the maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. Date Max (°F) Jun 1 80 Jun 2 82 Jun 3 81 Jun 4 75 Jun 5 76 Jun 6 71 Jun 7 82 Jun 8 85 Jun 9 86 Jun 10 77 Jun 11 75 Jun 12 78 Jun 13 85 Jun 14 82 Jun 15 86 Jun 16 90 Jun 17 92 Jun 18 92 Jun 19 89 Jun 20 85 Jun 21 72 Jun 22 81 Jun 23 79 Jun 24 85 Jun 25 79 Jun 26 79 Jun 27 81 Jun 28 85 Jun 29 89 Jun 30 92 Jul 1 93 Jul 2 90 Jul 3 89 Jul 4 92 Jul 5 92 Jul 6 81 Jul 7 79 Jul 8 86 Jul 9 89 Jul 10 91 Jul 11 83 Jul 12 83 Jul 13 89 Jul 14 90 Jul 15 90 Jul 16 86 Jul 17 86 Jul 18 83 Jul 19 83 Jul 20 73 Jul 21 76 Jul 22 80 Jul 23 78 Jul 24 79 Jul 25 85 Jul 26 84 Jul 27 78 Jul 28 80 Jul 29 78 Jul 30 76 Jul 31 76 Figure 2: Mean is given by, Mean = ∑Xi/n Here sample size is n= 61 ∑Xi= (80+82+81+…………..78+76+76) =5069 Mean = 5069/61 =83.09836066 The mean maximum daily temperature at Cox-Dayton International Airport for June and July 2018 is 83.098°F. Temperature Frequency Relative Frequency 70 - 74 3 3/61= 0.0492 75 - 79 16 16/61= 0.2623 80 - 84 15 15/61= 0.246 85 - 89 16 16/63=0.2623 90 - 94 11 11/61=0.1802 Total 61 1 How does the mean from the raw data (Figure 1) compare to the mean from the grouped data (Figure 2)?

Figure 1 The data are the maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. Date Max (°F) Jun 1 80 Jun 2 82 Jun 3 81 Jun 4 75 Jun 5 76 Jun 6 71 Jun 7 82 Jun 8 85 Jun 9 86 Jun 10 77 Jun 11 75 Jun 12 78 Jun 13 85 Jun 14 82 Jun 15 86 Jun 16 90 Jun 17 92 Jun 18 92 Jun 19 89 Jun 20 85 Jun 21 72 Jun 22 81 Jun 23 79 Jun 24 85 Jun 25 79 Jun 26 79 Jun 27 81 Jun 28 85 Jun 29 89 Jun 30 92 Jul 1 93 Jul 2 90 Jul 3 89 Jul 4 92 Jul 5 92 Jul 6 81 Jul 7 79 Jul 8 86 Jul 9 89 Jul 10 91 Jul 11 83 Jul 12 83 Jul 13 89 Jul 14 90 Jul 15 90 Jul 16 86 Jul 17 86 Jul 18 83 Jul 19 83 Jul 20 73 Jul 21 76 Jul 22 80 Jul 23 78 Jul 24 79 Jul 25 85 Jul 26 84 Jul 27 78 Jul 28 80 Jul 29 78 Jul 30 76 Jul 31 76 Figure 2: Mean is given by, Mean = ∑Xi/n Here sample size is n= 61 ∑Xi= (80+82+81+…………..78+76+76) =5069 Mean = 5069/61 =83.09836066 The mean maximum daily temperature at Cox-Dayton International Airport for June and July 2018 is 83.098°F. Temperature Frequency Relative Frequency 70 - 74 3 3/61= 0.0492 75 - 79 16 16/61= 0.2623 80 - 84 15 15/61= 0.246 85 - 89 16 16/63=0.2623 90 - 94 11 11/61=0.1802 Total 61 1 How does the mean from the raw data (Figure 1) compare to the mean from the grouped data (Figure 2)?

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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10.

Figure 1 The data are the maximum daily temperatures at Cox-Dayton International Airport for June and July 2018.

maximum daily temperatures at Cox-Dayton International Airport for June and July 2018.

Date	Max (°F)
Jun 1	80
Jun 2	82
Jun 3	81
Jun 4	75
Jun 5	76
Jun 6	71
Jun 7	82
Jun 8	85
Jun 9	86
Jun 10	77
Jun 11	75
Jun 12	78
Jun 13	85
Jun 14	82
Jun 15	86
Jun 16	90
Jun 17	92
Jun 18	92
Jun 19	89
Jun 20	85
Jun 21	72
Jun 22	81
Jun 23	79
Jun 24	85
Jun 25	79
Jun 26	79
Jun 27	81
Jun 28	85
Jun 29	89
Jun 30	92
Jul 1	93
Jul 2	90
Jul 3	89
Jul 4	92
Jul 5	92
Jul 6	81
Jul 7	79
Jul 8	86
Jul 9	89
Jul 10	91
Jul 11	83
Jul 12	83
Jul 13	89
Jul 14	90
Jul 15	90
Jul 16	86
Jul 17	86
Jul 18	83
Jul 19	83
Jul 20	73
Jul 21	76
Jul 22	80
Jul 23	78
Jul 24	79
Jul 25	85
Jul 26	84
Jul 27	78
Jul 28	80
Jul 29	78
Jul 30	76
Jul 31	76

Figure 2: Mean is given by,

Mean = ∑Xi/n

Here sample size is n= 61

∑Xi= (80+82+81+…………..78+76+76)

=5069

Mean = 5069/61

=83.09836066

The mean maximum daily temperature at Cox-Dayton International Airport for June and July 2018 is 83.098°F.

Temperature	Frequency	Relative Frequency
70 - 74	3	3/61= 0.0492
75 - 79	16	16/61= 0.2623
80 - 84	15	15/61= 0.246
85 - 89	16	16/63=0.2623
90 - 94	11	11/61=0.1802
Total	61	1

How does the mean from the raw data (Figure 1) compare to the mean from the grouped data (Figure 2)?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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