EXAMPLE 1. We have two sets of scores in a mathematics test given to grade 10 boys and girls. Here are the sets of scores with 100 as the highest possible score. 74 74 78 85 Вoys: 89 88 86 81 87 73 81 75 89 87 89 88 88 93 76 86 92 74 90 90 79 92 94 94 Girls: 72 78 75 78 75 90 76 72 92 85 76 71 86 75 96 71 74 76 87 74 80 81 75 74 71 76 71 71 Let us compare the two sets of scores of the boys and those of the girls by considering the statistical values, namely, the range, mean, and standard deviation. Boys Girls n, number of observation 28 28 range 94-73-21 96-71-25 x, mean of the distribution 84.71 77.79 S, standard deviation 6.84 6.90 Interpretation: The range of the scores of the boys is 21; the range of the scores of the girls is 25. There is a wider gap between the highest and lowest observations in the set of scores of the girls. A girl is the "top" scorer for this test, a 96. However, the lowest score of 71 for the test is found of the set of scores of the girls.28 girls who took the same test The mean, also called the average, of the 28 boys who took the math test is 84.71. This mean score is higher than 77.79, the mean of the 28 girls who took the same test. The mean difference in the scores in the test of the two groups is 6.92.
EXAMPLE 1. We have two sets of scores in a mathematics test given to grade 10 boys and girls. Here are the sets of scores with 100 as the highest possible score. 74 74 78 85 Вoys: 89 88 86 81 87 73 81 75 89 87 89 88 88 93 76 86 92 74 90 90 79 92 94 94 Girls: 72 78 75 78 75 90 76 72 92 85 76 71 86 75 96 71 74 76 87 74 80 81 75 74 71 76 71 71 Let us compare the two sets of scores of the boys and those of the girls by considering the statistical values, namely, the range, mean, and standard deviation. Boys Girls n, number of observation 28 28 range 94-73-21 96-71-25 x, mean of the distribution 84.71 77.79 S, standard deviation 6.84 6.90 Interpretation: The range of the scores of the boys is 21; the range of the scores of the girls is 25. There is a wider gap between the highest and lowest observations in the set of scores of the girls. A girl is the "top" scorer for this test, a 96. However, the lowest score of 71 for the test is found of the set of scores of the girls.28 girls who took the same test The mean, also called the average, of the 28 boys who took the math test is 84.71. This mean score is higher than 77.79, the mean of the 28 girls who took the same test. The mean difference in the scores in the test of the two groups is 6.92.
EXAMPLE 1. We have two sets of scores in a mathematics test given to grade 10 boys and girls. Here are the sets of scores with 100 as the highest possible score. 74 74 78 85 Вoys: 89 88 86 81 87 73 81 75 89 87 89 88 88 93 76 86 92 74 90 90 79 92 94 94 Girls: 72 78 75 78 75 90 76 72 92 85 76 71 86 75 96 71 74 76 87 74 80 81 75 74 71 76 71 71 Let us compare the two sets of scores of the boys and those of the girls by considering the statistical values, namely, the range, mean, and standard deviation. Boys Girls n, number of observation 28 28 range 94-73-21 96-71-25 x, mean of the distribution 84.71 77.79 S, standard deviation 6.84 6.90 Interpretation: The range of the scores of the boys is 21; the range of the scores of the girls is 25. There is a wider gap between the highest and lowest observations in the set of scores of the girls. A girl is the "top" scorer for this test, a 96. However, the lowest score of 71 for the test is found of the set of scores of the girls.28 girls who took the same test The mean, also called the average, of the 28 boys who took the math test is 84.71. This mean score is higher than 77.79, the mean of the 28 girls who took the same test. The mean difference in the scores in the test of the two groups is 6.92.
Compare the two sets of scorce using the range, mean, and standard deviation and interpret the results. See example 1.
Transcribed Image Text:EXAMPLE 1.
We have two sets of scores in a mathematics test given to grade 10 boys and girls. Here
are the sets of scores with 100 as the highest possible score.
74
79
92
Boys:
89
76
74
88
73
74
81
89
88
88
93
86
78
75
89
87
85
86
92
81
87
90
90
94
94
Girls:
72
78
75
78
75
92
85
71
86
75
96
71
74
76
87
74
80
81
90
76
76
76
71
75
74
71
71
72
Let us compare the two sets of scores of the boys and those of the girls by considering the
statistical values, namely, the range, mean, and standard deviation.
Вoys
Girls
n, number of observation
28
28
range
94-73-21
96-71 25
x, mean of the distribution
84.71
77.79
S, standard deviation
6.84
6.90
Interpretation:
The range of the scores of the boys is 21; the range of the scores of the girls is 25. There
is a wider gap between the highest and lowest observations in the set of scores of the girls, A girl
is the "top" scorer for this test, a 96. However, the lowest score of 71 for the test is found of the
set of scores of the girls.28 girls who took the same test
The mean, also called the average, of the 28 boys who took the math test is 84.71. This
mean score is higher than 77.79, the mean of the 28 girls who took the same test. The mean
difference in the scores in the test of the two groups is 6.92.
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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