Answer: 0.82 miles per gallon
Step-by-step explanation:
Given : Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (x) (in miles per gallon) of her car.
The results are :45 44 43 44 45 44 43
The formula to find the standard deviation is given by :-
[tex]\sigma=\sqrt{\dfrac{\sum_{i=1}^n(x_i-\overline{x})^2}{n-1}}[/tex]
First we find mean of the given data ,
[tex]\overline{x}=\dfrac{\sum^n_{i=1}x_i}{n}\\\\=\dfrac{45+44+43+44+45+44+43}{7}=\dfrac{308}{7}=44[/tex]
Now,
[tex]{\sum_{i=1}^n(x_i-\overline{x})^2=(1)^2+(0)^2+(-1)^2+(0)^2+(1)^2+(0)^2+(-1)^2[/tex]
[tex]=1+1+1+1=4[/tex]
Now, standard deviation of the above results will be :-
[tex]\sigma=\sqrt{\dfrac{4}{7-1}}\\\\=\sqrt{\dfrac{4}{6}}\\\\=\dfrac{2}{\sqrt{3}}=0.816496580928\approx0.82[/tex]
Hence, the standard deviation of these results = 0.82 miles per gallon
