Respuesta :
Answer:
The sample mean is 73.8
The sample variance is 689.1
Explanation:
This a grouped data question.
A. To calculate Sample Mean, we follow the following steps:
Step A1. Calculate the midpoint of the Heart Rates in Beats per Minute
For 51 - 58, the midpoint is (54 + 55) ÷ 2 = 54.5
For 59 - 66, the midpoint is (62 + 63) ÷ 2 = 62.5
For 67 - 74 , the midpoint is (70 + 71) ÷ 2 = 70.5
For 75 - 82, the midpoint is (78 + 79) ÷ 2 = 78.5
For 83 - 90, the midpoint is (86 + 87) ÷ 2 = 86.5
Step A2. Multiply the midpoint of the Heart Rates in Beats per Minute by the frequency
For 51 - 58, (54.5) × (6) = 327
For 59 - 66, (62.5) × (3) = 188
For 67 - 74 , (70.5) × (11) = 776
For 75 - 82, (78.5) × (13) = 1,021
For 83 - 90, (86.5) × (4) = 346
Step A3. Add answers in Step A2 and divide by the sum of the frequency minus 1
U = (327 + 188 + 776 + 1,021 + 346) ÷ ((6 + 3 + 11 + 13 + 4 + 37) - 1)
= 2,657 ÷ 36
= 73.8
Where U represents the sample mean which is 71.8.
B. To calculate Sample Variance, we follow the following steps:
B.1. Subtract mean from each of the midpoints
For 51 - 58, (54.5) - (73.8) = -19.3
For 59 - 66, (62.5) - (73.8) = -11.3
For 67 - 74 , (70.5) - (73.8) = -144.3
For 75 - 82, (78.5) - (73.8) = 5.7
For 83 - 90, (86.5) - (73.8) = 13.7
B.2. Add the answers above and squared
D^2 = (- 19 - 11 - 144 + 5 + 13)^2
= (-157.5)^2
= 24,806.3
B.2. Divide D^2 by sum of the frequency minus 1
S^2 = 24,806.3 ÷ 36
= 689.1
Where S^2 represents the sample variance which is 689.1.
Therefore, the sample mean is 73.8 and the sample variance is 689.1
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