Question

In Amihan’s backyard,there are six trees, whosemeasurements she records as 4.26 m, 2.13 m, 2.44 m, 3.05 m, 2.74 m, and 2.29 m. Determine the standard deviation of height of the trees.​

Answer 1

Given data:

The heights of the six tress are $\mathsf{4.26}$ m, $\mathsf{2.13}$ m, $\mathsf{2.44}$ m, $\mathsf{3.05}$ m, $\mathsf{2.74}$ m and $\mathsf{2.29}$ m

To find:

Stands deviation of height of the trees

Step-by-step explanation:

First we find the mean (μ), which is given by

$\quad\mathsf{\mu=\dfrac{4.26 + 2.13 + 2.44 + 3.05 + 2.74 + 2.29}{6}}$

$\mathsf{\Rightarrow\mu=\dfrac{16.91}{6}}$

$\mathsf{\Rightarrow\mu=2.8183}$

Now we find the standard deviation (σ) of height of the trees.

$\quad\mathsf{\sigma=\sqrt{\dfrac{(4.26-2.8183)^{2}+(2.13-2.8183)^{2}+(2.44-2.8183)^{2}+(3.05-2.8183)^{2}+(2.74-2.8183)^{2}+(2.29-2.8183)^{2}}{6}}}$

$\mathsf{\Rightarrow\sigma=\sqrt{\dfrac{3.0343}{6}}}$

$\mathsf{\Rightarrow\sigma=\sqrt{0.50572}}$

$\mathsf{\Rightarrow\sigma=0.71}$

Answer: Standard deviation = 0.71

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