Answer:
The median : 9
The range: 5
The mode: 7
Step-by-step explanation:
We are given the data set: [tex]7,7,7,8,10,11,12,12[/tex] and are asked to find the median, range and mode. Let's start with the median.
Median:
Start by arranging the data set in numerical order:
[tex]7,7,7,8,10,11,12,12[/tex]
Now from here, you can count the number of terms(8). When there are an even number of terms, the average of the middle value and the value following the middle value make the median. This means that the 4th and 5th term average to the median.
[tex]7,7,7,\boxed{8,10},11,12,12[/tex]
Now from here, add up the terms and divide by two to get its average:
[tex]\[ \frac{8 + 10}{2} = \frac{18}{2} = \boxed{9} \][/tex]
Therefore, the median is 9.
Range:
Range is very simple. All you need to do is subtract the highest term from the lowest term.
In this case, 12 is the highest term, and 7 is the lowest.
[tex]\text{Range:} ~ 12-7 = \boxed{5}[/tex]
Therefore, the range is 5
Mode:
Mode represents the term that appears the most in the data set.
[tex]\text{\item \textbf{7} appears \textbf{3} ~times} \item \textbf{8} appears \textbf{1} time \item \textbf{10} appears \textbf{1} time \item \textbf{11} appears \textbf{1} time \item \textbf{12} appears \textbf{2} times[/tex]
Notice how 7 appears 3 times? That is the highest amount of occurrences making it the mode.
