Final answer:
To find the variance and standard deviation of the set V(11,13,15,17,19), calculate the mean, square the deviations of each value from the mean, and then compute the average of these squares to get the variance. The standard deviation is the square root of the variance. The correct answer is Variance: 8 and Standard Deviation: 2.83.
Step-by-step explanation:
To find the variance and standard deviation of the set V(11,13,15,17,19), we must first calculate the mean (average) of these numbers. We then use this mean to find the deviation of each individual number in the set, square these deviations, and calculate the average of these squared deviations to find the variance. The standard deviation is then the square root of the variance.
The mean of the set V is (11 + 13 + 15 + 17 + 19) / 5 = 75 / 5 = 15.
The deviations from the mean for each number in the set V are:
- 11: 15 - 11 = 4
- 13: 15 - 13 = 2
- 15: 15 - 15 = 0
- 17: 15 - 17 = -2
- 19: 15 - 19 = -4
The squared deviations are therefore 16, 4, 0, 4, and 16, respectively.
The variance is the mean of these squared deviations: (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8.
The standard deviation is the square root of the variance: √8 ≈ 2.83.
Therefore, the correct answer is c. Variance: 8 Standard Deviation: 2.83.