Question

Find the range and standard deviation of the set of data.4, 7, 4, 7, 7, 9, 11The range is(Simplify your answer.)

Answer 1

SOLUTI0N

Step 1 :

In this question, we are meant to find the range and standard deviation of the set of the data:

4, 7, 4, 7, 7, 9, 11

For the Range, we have that:

`\begin{gathered} \text{Range = Highest number - Smallest number } \\ =\text{ 11 - 4} \\ =7 \end{gathered}`

Step 2 :

For the Standard Deviation,

We have that :

`\text{Standard Deviation =}\frac{\sqrt[]{\sum ^(\infty)_(n\mathop=0)(X_{i\text{ }}-X)^2}}{n}`

So, we need to evaluate using the following process,

`\begin{gathered} \text{Mean, X = }\frac{4\text{ + 7 + 4 + 7 +7 + 9 + 11}}{7} \\ =(49)/(7) \\ =\text{ 7} \end{gathered}`

Next, we evaluate the following :

Variance =

`((4-7)^2+(7-4)^2+(4-7)^2+(7-7)^2+(7-7)^2+(9-7)^2+(11-7)^2)/(7)`

=

`\begin{gathered} \frac{9\text{ + 9 + 9 + 0 + 0 + 4 + 4}}{7} \\ =\text{ }(35)/(7) \\ =\text{ 5} \end{gathered}`

Next, we have that :

Standard Deviation =

`\sqrt[\square]{Variance}`

=

`\begin{gathered} \sqrt[\square]{5} \\ =\text{ 2. 236} \\ =\text{ 2. 2}4\text{ ( nearest hundredth )} \end{gathered}`

CONCLUSION:

The Range = 7 and the Standard Deviation = 2. 24