Question

If n=18,then the pair of Ƭ(18) and σ(18) is :​

Answer 1

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Answer 2

Question:

If for distribution of 18 observations $\sum\left(x_{i}-5\right)=3$ and $\sum\left(x_{i}-5\right)^{2}=43$

find the mean and standard deviation (Ƭ(18) and σ(18)).

Answer:

The pair of Ƭ(18) and σ(18) is,

Ƭ(18) = 5.17 and

σ(18) = 1.59.

Step-by-step explanation:

Given:

$n=18$

$\sum\left(x_{i}-5\right)=3$ and

$\sum\left(x_{i}-5\right)^{2}=43$

To find Ƭ(18) and σ(18).

Step 1

Ƭ(18) = $Mean=A+\frac{\Sigma(x-5)}{18}$

$=5+\frac{3}{18}$

$=5+0.1666$

$=5.1666$

$=5.17$

Step 2

σ(18) = $S D=\sqrt{\frac{\Sigma(x-5)^{2}}{n}}-\left(\frac{\Sigma(x-5)}{n}\right)^{2}$

$=\sqrt{\frac{43}{18}-\left(\frac{3}{18}\right)^{2}}$

$=\sqrt{2.3944-(0.166)^{2}}$

$=\sqrt{2.3944-0.2755}$

$=1.59$

Therefore,

Mean = Ƭ(18) = 5.17

Standard deviation = σ(18) = 1.59