The midrange of a data set is the mean of its least and greatest elements. The midrange of the first data set is \(\displaystyle \left (10,000 + 1 \right ) \div 2 = 5,000.5\); that of the second data set is \(\displaystyle (80 + 120) \div 2 = 100\). (A) is greater.

To find the range of a set of numbers, you do not even have to put them in order.  You merely need to subtract the smallest value from the largest.  Given the way of constructing set \(\displaystyle T\) by doubling set \(\displaystyle S\)'s values, the largest and smallest values in \(\displaystyle T\) will directly correlate to the same in set \(\displaystyle S\):

Smallest: \(\displaystyle 1 => 2\) 

Largest: \(\displaystyle 13=>26\)

Therefore, the range  is: \(\displaystyle 26-2=24\)

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set \(\displaystyle S\) from the function \(\displaystyle f(x)\), we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be \(\displaystyle f(0)\) and the largest will be \(\displaystyle f(13)\)

Smallest: \(\displaystyle f(0) = 0^2 + 3 = 3\) 

Largest: \(\displaystyle f(13) = 13^2 + 3 = 172\)

Therefore, the range  is: \(\displaystyle 172 - 3 = 169\)

We first need to determine the members of set \(\displaystyle T\). Using our function, we will get:

\(\displaystyle f(13) = 130\)

\(\displaystyle f(-1) = (-1)^2-3(-1)=1+3=4\)

\(\displaystyle f(4) = (4)^2-3(4)=16-12=4\) 

\(\displaystyle f(1) = (1)^2-3(1)=1-3=-2\)

\(\displaystyle f(-9) = (-9)^2-3(-9)=81+27=108\)

\(\displaystyle f(10) = (10)^2-3(10)=100-30=70\)

Our largest value is \(\displaystyle 130\), and our smallest value is \(\displaystyle -2\); therefore, the range is \(\displaystyle 130-(-2)= 130+2=132\)

Range for a set of data is defined as the difference between the biggest and smallest number. 

First we find the biggest number which is 15, we then subtract the smallest number in this set which is negative 2 as shown below: 

\(\displaystyle 15-(-2) = 15 + 2 = 17\)

Remember, when subtracting a negative number we must add the numbers. 

In order to find the range, we must subtract the smallest number from the biggest number. 

\(\displaystyle Biggest\ Number = \frac{4}{5}\)

\(\displaystyle Smallest\ Number = \frac{1}{10}\)

\(\displaystyle \frac{4}{5}-\frac{1}{10}\)

We must convert the fractions to have a common denominator which is 10. 

\(\displaystyle \frac{8}{10}-\frac{1}{10}=\frac{7}{10}\)

Therefore, the range of this set is

\(\displaystyle \frac{7}{10}\).

In order to find the range, we must subtract the smallest number from the biggest number. 

\(\displaystyle Biggest\ Number = \frac{4}{5}\)

\(\displaystyle Smallest\ Number = \frac{1}{10}\)

\(\displaystyle \frac{4}{5}-\frac{1}{10}\)

We must convert the fractions to have a common denominator which is 10. 

\(\displaystyle \frac{8}{10}-\frac{1}{10}=\frac{7}{10}\)

Therefore, the range of this set is

\(\displaystyle \frac{7}{10}\).

In order to answer this question correctly, we need to recall the definition of range:

Range: The range of a data set is the difference between the highest value and the lowest value in the set. 

In order to find the range, we need to first organize the data from least to greatest to find the lowest and highest values:

\(\displaystyle 26,26,26,27,28,28,28,29,30,30,30,31,32,33,34,34,34,34,35,36\)

Next, we can solve for the difference between the highest value and the lowest value:

\(\displaystyle \frac{\begin{array}[b]{r}36\\ -\ 26\end{array}}{ \ \ \ \space 10}\)

The range for this data set is \(\displaystyle 10\)

In order to answer this question correctly, we need to recall the definition of range:

Range: The range of a data set is the difference between the highest value and the lowest value in the set. 

In order to find the range, we need to first organize the data from least to greatest to find the lowest and highest values:

\(\displaystyle 11,11,13,14,14,14,14,15,18,19,20,20,21,22,27\)

Next, we can solve for the difference between the highest value and the lowest value:

\(\displaystyle \frac{\begin{array}[b]{r}27\\ -\ 11\end{array}}{ \ \ \ \space 16}\)

The range for this data set is \(\displaystyle 16\)

In order to answer this question correctly, we need to recall the definition of range:

Range: The range of a data set is the difference between the highest value and the lowest value in the set. 

In order to find the range, we need to first organize the data from least to greatest to find the lowest and highest values:

\(\displaystyle 1,2,3,3,4,4,4,4,5,7,8,9,10,10,11\)

Next, we can solve for the difference between the highest value and the lowest value:

\(\displaystyle \frac{\begin{array}[b]{r}11\\ -\ 1\end{array}}{ \ \ \ \space 10}\)

The range for this data set is \(\displaystyle 10\)