Question

Calculate the standard deviation. plant height [in cm]x,2,3,6,5,9​

Answer 1

Answer:

use formula standard deviation = square root of ((sigma x^2/n -(sigma x/n)^2)

Answer 2

Given:

The height of 5 plants (in cm) are given.

Height of 5 plants = 2 cm, 3 cm, 6 cm, 5 cm, and 9​ cm.

Number of plants, N = 5.

To Find:

In order to calculate the standard deviation, the height of plants is taken as Xi. Then the square of each value of Xi is found out as in the table below.

Solution:

From the table,

Σ$X_{i} = 25.$

Σ$(X_{i}) ^{2} = 155.$

The formula for finding Standard deviation is given by:

σ = $\sqrt{\frac{Σ(X_{i}) ^{2} }{N}-(\frac{ΣX_{i} }{N}) ^{2} }$

Substitute Σ$X_{i}$ and Σ$(X_{i}) ^{2}$ in above equation to get,

σ = $\sqrt{\frac{155}{5}-(\frac{25}{5} )^{2} }$

$= \sqrt{\frac{155}{5}-\frac{625}{25} } \\= \sqrt{\frac{155.5}{5.5}-\frac{625}{25} } \\= \sqrt{\frac{775}{25}-\frac{625}{25} } \\= \sqrt{\frac{775-625}{25} } \\= \sqrt{\frac{150}{25} } \\= \sqrt{6} \\= 2.45 cm$

Hence the standard deviation of plants with height 2 cm, 3 cm, 6 cm, 5 cm, and 9​ cm is 2.45 cm.

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