Final answer:
To calculate the sample standard deviation of the heights of 10 adult males, one must find the mean, determine the squared differences from the mean, sum these squared differences, divide by the number of observations minus one, and finally take the square root. The calculated standard deviation is approximately 1.49 inches.
Step-by-step explanation:
The question asks us to find the sample standard deviation of the heights of 10 adult males. The given data set is: 70, 72, 71, 70, 69, 73, 69, 68, 70, 71 inches.
- Calculate the sample mean (μ): (70+72+71+70+69+73+69+68+70+71) / 10 = 70.3 inches.
- Subtract the mean from each data point and square the result: (0.3)^2, (1.7)^2, (0.7)^2, (0.3)^2, (-1.3)^2, (2.7)^2, (-1.3)^2, (-2.3)^2, (0.3)^2, (0.7)^2.
- Sum these squared differences: 0.09 + 2.89 + 0.49 + 0.09 + 1.69 + 7.29 + 1.69 + 5.29 + 0.09 + 0.49 = 20.1.
- Divide this sum by the sample size minus one (n-1), which is 9: 20.1 / 9 = 2.2333.
- Take the square root to find the sample standard deviation: √2.2333 = 1.4944 inches.
The sample standard deviation of this data set is approximately 1.49 inches, which corresponds to option A.