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Ganezh [65]
3 years ago
13

Jenna has bought a new hybrid car. Each week for a period of seven weeks, she has noted the fuel efficiency (in miles per gallon

) of her car.
The results are shown below. 45 44 43 44 45 44 43 6. Calculate the standard deviation of these results to the nearest hundredth. Be sure to show your work.
Mathematics
1 answer:
Leviafan [203]3 years ago
8 0

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 :-

\sigma=\sqrt{\dfrac{\sum_{i=1}^n(x_i-\overline{x})^2}{n-1}}

First we find mean of the given data ,

\overline{x}=\dfrac{\sum^n_{i=1}x_i}{n}\\\\=\dfrac{45+44+43+44+45+44+43}{7}=\dfrac{308}{7}=44

Now,

{\sum_{i=1}^n(x_i-\overline{x})^2=(1)^2+(0)^2+(-1)^2+(0)^2+(1)^2+(0)^2+(-1)^2

=1+1+1+1=4

Now,  standard deviation of the above results will be :-

\sigma=\sqrt{\dfrac{4}{7-1}}\\\\=\sqrt{\dfrac{4}{6}}\\\\=\dfrac{2}{\sqrt{3}}=0.816496580928\approx0.82

Hence, the standard deviation of these results = 0.82 miles per gallon

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<h3>What is the percentage?</h3>

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

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Month         Payment         Principal         Interest         Balance

  15               236.72            155.87            80.85           8704.27

  16               236.72            157.29            79.43           8546.98

  17               236.72            158.73            77.99            8388.25

  18               236.72            160.18            76.54            8228.07

  19               236.72            161.64            75.08            80.66.43

  20              236.72            163.11             73.61             7903.32

Total payment = 6 × 236.72 = $ 1420.32

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\rm Percentage = \dfrac{463.38}{1420.32}*100\\\\Percentage = 32.625 \approx  32.6\ \%

More about the percentage link is given below.

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