The first position can be filled 10 ways and since repetition is allowed, the 2nd position can be filled in 10 ways and similarly the third position can be filled in 10 ways as well, giving us the correct answer of

\(\displaystyle 10^{3}\)

The range is the difference between the lowest and the highest number in the number set.

The lowest number in the number set is 2 while the highest number is 10. Therefore, the range is calculated as

\(\displaystyle 10-2=8\)

So 8 is the range.

This is a combination problem.  All we need to solve this problem is the combination formula: \(\displaystyle C\binom{n}{k}=\frac{n!}{k!(n-k)!}\)

\(\displaystyle C\binom{5}{3} = \frac{5!}{2!\times 3!}\)

Now \(\displaystyle 5! = 5\times 4\times 3\times 2\times\times 1\)

\(\displaystyle 3!= 3\times 2\times 1\)

and \(\displaystyle 2! = 2\times 1\)

Instead of finding answers for all of these factorials, notice that they have many of the same terms and can therefore be cancelled.

\(\displaystyle \frac{5\times 4\times3\times2\times1}{3\times2\times1\times2\times1}=\frac{5\times4}{2}=5\times2=10\)

The range of the statistics is simply the difference between the largest value and the smallest value.

The largest number in the set is 98, and the smallest number is 68.

Subtract to find the range:

\(\displaystyle 98-68=30\)

The range is the difference between the smallest number and the largest number. The smallest value is 77, and the largest is 98.

98 – 77 = 21

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

The range is difference between the largest value and the smallest value.

\(\displaystyle Largest=\$40\)

\(\displaystyle Smallest=\$15\)

\(\displaystyle Range=Largest-Smallest=\$40-\$15=\$25\)

The range is defined as the difference between the highest and lowest numbers in a set. Here, the highest number is \(\displaystyle 25\) and the lowest is \(\displaystyle -2\). 

Therefore, the range is

 \(\displaystyle 25 - (-2)=27\)

\(\displaystyle -2\) is the mode, \(\displaystyle 7.9\) is the mean, and 6 is the median.

To determine the range of this data set, take the largest number and subtract it with the smallest number.

The largest number in the set is ten.

The smallest number in the set is \(\displaystyle -5\).

Subtract both numbers.

\(\displaystyle 10-(-5)= 10+5=15\)

Subtract the lowest number (4) from the highest (52) to get 48.

\(\displaystyle 24, 4, {\color{Red}{52}}, 39, 23, 25, 48, 12, {\color{Red} 4}\)

\(\displaystyle 52-4=48\)