Question

Listed below are pulse rates​ (beats per​ minute) from samples of adult males and females. Does there appear to be a​ difference? Find the coefficient of variation for each of the two​ samples; then compare the variation.

Male Female89 6871 8060 8068 7070 7650 8662 8756 8482 8768 8762 9461 70100 8756 8165 77

Answer 1

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.

Answer 2

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%

Explanation:

Mean (male) =
`(sum of x)/(n) =(1020)/(16) =63.75`

Mean (female) =
`(sum of y)/(n) = (1214)/(16) = 75.875`

Standard Deviation (male) =
`\sqrt{(sum(x-63.75)^2)/(16-1) } =21.315`

Standard Deviation (female) =
`\sqrt{(sum(y-75.875)^2)/(16-1) } = 21.512`

Coefficient of Variation =
`(Std dev)/(mean) *100`

For male, CV =
`(21.315)/(63.75) *100=33.44%`%

For female, CV =
`(21.512)/(75.875) *100=28.35`%

Comparison : Pulse rates of males has more variability than that of females since it has a greater coefficient of variation.