Question

1. WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA. ROUND YOUR ANSWER TO TWO DECIMAL PLACES 6 8 5 11 4 22.WHAT IS THE STANDARD DEVIATION FOR THE FOLLOWING DATA.90 90 90 90 90 90?3.) IF THE STANDARD DEVIATION IS 9, WHAT IS THE VARIANCE?

Answer 1

Solution:3.16

Analysis: In the first step, we need to find the mean of values we have in the exercise:

$Mean=(6+8+5+11+4+2)/6=36/6=6$

Now, let's find the standard deviation:

Subtract the mean from each of the data values and list the differences.

6-6=0

8-6=2

5-6=-1

11-6=5

4-6=-2

2-6=-4

Now, let's square each of the differences from the previous step and make a list of the squares.

$\begin{gathered} 0^2=0 \\ 2^2=4 \\ (-1)^2=1 \\ 5^2=25 \\ (-2)^2=4 \\ (-4)^2=16 \\ \end{gathered}$

Now, let's add the squares from the previous step:

0+4+1+25+4+16=50.

Let's use the formula

$S=\sqrt{\frac{\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}}=\sqrt{\frac{50^{}}{6-1}}=\sqrt{10}=3.16$