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Answer :
We begin by finding the sample mean of the data set. The data is
$$
129,\ 131,\ 128,\ 123,\ 124,\ 129,\ 139,\ 139.
$$
1. Calculate the sample mean ($\bar{x}$):
$$\bar{x} = \frac{129 + 131 + 128 + 123 + 124 + 129 + 139 + 139}{8} = 130.25.$$
2. Next, compute the squared differences for each data value from the mean:
\[
\begin{aligned}
(129 - 130.25)^2 & = 1.5625,\\[1mm]
(131 - 130.25)^2 & = 0.5625,\\[1mm]
(128 - 130.25)^2 & = 5.0625,\\[1mm]
(123 - 130.25)^2 & = 52.5625,\\[1mm]
(124 - 130.25)^2 & = 39.0625,\\[1mm]
(129 - 130.25)^2 & = 1.5625,\\[1mm]
(139 - 130.25)^2 & = 76.5625,\\[1mm]
(139 - 130.25)^2 & = 76.5625.
\end{aligned}
\]
3. Sum these squared differences:
$$\text{Total} = 1.5625 + 0.5625 + 5.0625 + 52.5625 + 39.0625 + 1.5625 + 76.5625 + 76.5625 = 253.5.$$
4. Since this is a sample, we divide by $n-1$ (with $n = 8$) to find the sample variance:
$$s^2 = \frac{253.5}{8-1} = \frac{253.5}{7} \approx 36.2143.$$
5. Finally, the sample standard deviation is the square root of the variance:
$$s = \sqrt{36.2143} \approx 6.0178.$$
Rounding to the nearest hundredth, we obtain:
$$s \approx 6.02.$$
Thus, the sample standard deviation is approximately $$\boxed{6.02}.$$
$$
129,\ 131,\ 128,\ 123,\ 124,\ 129,\ 139,\ 139.
$$
1. Calculate the sample mean ($\bar{x}$):
$$\bar{x} = \frac{129 + 131 + 128 + 123 + 124 + 129 + 139 + 139}{8} = 130.25.$$
2. Next, compute the squared differences for each data value from the mean:
\[
\begin{aligned}
(129 - 130.25)^2 & = 1.5625,\\[1mm]
(131 - 130.25)^2 & = 0.5625,\\[1mm]
(128 - 130.25)^2 & = 5.0625,\\[1mm]
(123 - 130.25)^2 & = 52.5625,\\[1mm]
(124 - 130.25)^2 & = 39.0625,\\[1mm]
(129 - 130.25)^2 & = 1.5625,\\[1mm]
(139 - 130.25)^2 & = 76.5625,\\[1mm]
(139 - 130.25)^2 & = 76.5625.
\end{aligned}
\]
3. Sum these squared differences:
$$\text{Total} = 1.5625 + 0.5625 + 5.0625 + 52.5625 + 39.0625 + 1.5625 + 76.5625 + 76.5625 = 253.5.$$
4. Since this is a sample, we divide by $n-1$ (with $n = 8$) to find the sample variance:
$$s^2 = \frac{253.5}{8-1} = \frac{253.5}{7} \approx 36.2143.$$
5. Finally, the sample standard deviation is the square root of the variance:
$$s = \sqrt{36.2143} \approx 6.0178.$$
Rounding to the nearest hundredth, we obtain:
$$s \approx 6.02.$$
Thus, the sample standard deviation is approximately $$\boxed{6.02}.$$
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