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:
[tex]\begin{gathered} \text{Range = Highest number - Smallest number } \\ =\text{ 11 - 4} \\ =7 \end{gathered}[/tex]Step 2 :
For the Standard Deviation,
We have that :
[tex]\text{Standard Deviation =}\frac{\sqrt[]{\sum ^{\infty}_{n\mathop=0}(X_{i\text{ }}-X)^2}}{n}[/tex]So, we need to evaluate using the following process,
[tex]\begin{gathered} \text{Mean, X = }\frac{4\text{ + 7 + 4 + 7 +7 + 9 + 11}}{7} \\ =\frac{49}{7} \\ =\text{ 7} \end{gathered}[/tex]Next, we evaluate the following :
Variance =
[tex]\frac{(4-7)^2+(7-4)^2+(4-7)^2+(7-7)^2+(7-7)^2+(9-7)^2+(11-7)^2}{7}[/tex]=
[tex]\begin{gathered} \frac{9\text{ + 9 + 9 + 0 + 0 + 4 + 4}}{7} \\ =\text{ }\frac{35}{7} \\ =\text{ 5} \end{gathered}[/tex]Next, we have that :
Standard Deviation =
[tex]\sqrt[\square]{Variance}[/tex]=
[tex]\begin{gathered} \sqrt[\square]{5} \\ =\text{ 2. 236} \\ =\text{ 2. 2}4\text{ ( nearest hundredth )} \end{gathered}[/tex]CONCLUSION:
The Range = 7 and the Standard Deviation = 2. 24
