Respuesta :
Answer:
There appears to be a difference between the pulse rates from samples of adult males and females. The average pulse rate of males is 63.75 while that of females is 75.875.
Coefficient of Variation (male) = 33.44%
Coefficient of variation (female) = 28.35%
Step-by-step explanation:
Mean (male) = [tex]\frac{sum of x}{n} =\frac{1020}{16} =63.75[/tex]
Mean (female) = [tex]\frac{sum of y}{n} = \frac{1214}{16} = 75.875[/tex]
Standard Deviation (male) = [tex]\sqrt{\frac{sum(x-63.75)^2}{16-1} } =21.315[/tex]
Standard Deviation (female) = [tex]\sqrt{\frac{sum(y-75.875)^2}{16-1} } = 21.512[/tex]
Coefficient of Variation = [tex]\frac{Std dev}{mean} *100[/tex]
For male, CV = [tex]\frac{21.315}{63.75} *100=33.44%[/tex]%
For female, CV = [tex]\frac{21.512}{75.875} *100=28.35[/tex]%
Comparison : Pulse rates of males has more variability than that of females since it has a greater coefficient of variation.
Answer / Step-by-step explanation:
FOR MALE
Mean for male pulse rate:
Xˣ = ∑ x / n
86 + 72 + 64 + 72 + 72 + 54 + 66 + 56 + 80 + 72 + 64 + 64 + 96 + 58 + 66 / 15
= 1042 / 15
= 69.4667
Approximately, we have = 69.5
Variance for the male pulse rate:
S² = ∑ (x - xˣ )² / n - 1
= (86 - 69.5)² + (72 - 69.5)² + (64 - 69.5)² + (72 - 69.5)² + (72 - 69.5)² + (54 - 69.5)² + (66 - 69.5)² + (56 - 69.5)² + (80 - 69.5)² + (72 - 69.5)² + (64 - 69.5)² + (64 - 69.5)² + (96 - 69.5)² + (58 - 69.5)² + (66 - 69.5)² / 15 - 1
= 272.25 + 6.25 + 30.25 + 6.25 + 6.25 + 240.25 + 12.25 + 182.25 + 110.25 + 6.25 + 30.25 + 702.25 + 132.25 + 12.25 / 14
= 1779.75 / 14
127 . 12
Standard Deviation for the male pulse rate:
S = √ ∑ n ( ∑ x² ) - (∑ x )² / n (n - 1)
Therefore, s = √s²
S = √ 127.12
S = 11.3
Coefficient of variation:
CV = S / X
= 11.2749 / 69.4667
= 0.1623. Converting to percentage, we have: 16.23%
FOR FEMALE
Mean for Female pulse rate:
Xˣ = ∑ x / n
= 64 + 84 + 82 + 70 + 74 + 86 + 90 + 88 + 90 + 90 + 94 + 68 + 90 + 82 + 80 / 15
= 1232 / 15
= 82 . 1333
Variance for the female pulse rate:
S² = ∑ (x - xˣ )² / n - 1
= (64 - 82.1333)² + (84 - 82.1333)² + (82 - 82.1333)² + (70 - 82.1333)² + (74 - 82.1333)² + (86 - 82.1333)² + (90 - 82.1333)² + (88 - 82.1333)² + (90 - 82.1333)² + (90 - 82.1333)² + (94 - 82.1333)² + (68 - 82.1333)² + (90 - 82.1333)² + (82 - 82.1333)² + (80 - 82.1333)² / 15 - 1
Calculating further, we arrive at
= 84.8381
Standard Deviation for the female pulse rate:
S = √ ∑ n ( ∑ x² ) - (∑ x )² / n (n - 1)
Therefore, s = √s²
S = √ 84.8381
S = 9.2108
Coefficient of variation:
CV = S / X
= 9.2108 / 82.1333
= 0.1121. Converting to percentage, we have: 11.21%
Now, to compare, we can see that the variation for female pause rate appears to be lower than the variation for male pulse rate.
