Mathematics: How do write this algebraic expression? s + 7

How do write this algebraic expression? s + 7

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s11632270

17.05.2022

Mathematics

The mean, median, and standard deviation of the University of Oregon are $451.33, $467.5, and $113.61 respectively.

The mean, median, and standard deviation of the University of Washington are $396.67, $380, and $56.27 respectively.

Step-by-step explanation:

We are given that a sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Oregon is: $295, $475, $345, $595, $538, $460.

A second sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Washington is: $495, $422, $370, $333, $370, $390.

Firstly, we will calculate the mean, median, and standard deviation for the data of the University of Oregon.

Arranging the data in ascending order we get;

X = $295, $345, $460, $475, $538, $595.

The mean of the above data is given by the following formula;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{\$295+ \$345+ \$460+\$475+ \$538+\$595}{6}$

= $\frac{\$2708}{6}$ = $451.33

So, the mean price of rent near the University of Oregon is $451.33.

For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.

If n is odd, then the formula for calculating median is given by;

Median = $(\frac{n+1}{2} )^{th} \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}$

Here, the number of observations is even, i.e. n = 6.

So, Median = $\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}$

= $\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}$

= $\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}$

= $\frac{\$460 +\$475}{2}$ = $467.5

Hence, the median price of rent for the University of Oregon is $467.5.

Now, the standard deviation is calculated by using the following formula;

Standard deviation, S.D. = $\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }$

= $\sqrt{\frac{ (\$295 - \$451.33)^{2} +(\$345 - \$451.33)^{2} +......+(\$595 - \$451.33)^{2} }{6-1} }$

= $113.61

So, the standard deviation for the University of Oregon is $113.61.

Now, we will calculate the mean, median, and standard deviation for the data of the University of Washington.

Arranging the data in ascending order we get;

X = $333, $370, $370, $390, $422, $495.

The mean of the above data is given by the following formula;

Mean, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{\$333+ \$370+ \$370+\$390+ \$422+\$495}{6}$

= $\frac{\$2380}{6}$ = $396.67

So, the mean price of rent near the University of Washington is $396.67.

For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.

If n is odd, then the formula for calculating median is given by;

Median = $(\frac{n+1}{2} )^{th} \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}$

Here, the number of observations is even, i.e. n = 6.

So, Median = $\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}$

= $\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}$

= $\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}$

= $\frac{\$370 +\$390}{2}$ = $380

Hence, the median price of rent for the University of Washington is $380.

Now, the standard deviation is calculated by using the following formula;

Standard deviation, S.D. = $\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }$

= $\sqrt{\frac{ (\$333 - \$396.67)^{2} +(\$370 - \$396.67)^{2} +......+(\$495 - \$396.67)^{2} }{6-1} }$

= $56.27

So, the standard deviation for the University of Washington is $56.27.

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