Explanation:
Let's calculate the standard deviation.

1. Calculate the Mean:
The mean height is:
\[
\text{Mean} = \frac{145 + 163 + 159 + 162 + 167 + 149 + 150 + 160 + 170 + 155}{10} = \frac{1,580}{10} = 158
\]

2. Calculate Each Squared Difference from the Mean:
\[
(145 - 158)^2 = (-13)^2 = 169
\]
\[
(163 - 158)^2 = 5^2 = 25
\]
\[
(159 - 158)^2 = 1^2 = 1
\]
\[
(162 - 158)^2 = 4^2 = 16
\]
\[
(167 - 158)^2 = 9^2 = 81
\]
\[
(149 - 158)^2 = (-9)^2 = 81
\]
\[
(150 - 158)^2 = (-8)^2 = 64
\]
\[
(160 - 158)^2 = 2^2 = 4
\]
\[
(170 - 158)^2 = 12^2 = 144
\]
\[
(155 - 158)^2 = (-3)^2 = 9
\]

Sum of squared differences:
\[
169 + 25 + 1 + 16 + 81 + 81 + 64 + 4 + 144 + 9 = 594
\]

Calculate the Variance:
\[
\text{Variance} = \frac{504}{10} = 59.4
\]

Calculate the Standard Deviation:
\[
\text{Standard Deviation} = \sqrt{59.4} \approx 7.7
\]


The corrected standard deviation of the heights is approximately 7.7cm.