The scores represented can be found from matching the tens digits in the "stem" to the units digits that form the "leaves" in their row. For example, the "leaves" in the "5" row are "2 2 4 4 7 7 8", so the scores will be 52, 52, 54, 54, 57, 57, and 58.

There are 53 scores represented, so to find the median, look for the middle score, in position

\(\displaystyle \frac{53+1}{2} = 27\).

As can be seen in this diagram, the score - the median - is 74.

The most frequently occurring "leaf" is the "6" in the "7" row, so the mode is 76.

The mean is the sum of the scores divided by 53. If we add the scores, we get

\(\displaystyle \sum x = 3,763\), the mean is

\(\displaystyle \frac{\sum x }{n}=\frac{ 3,763}{53} = 71\)

In ascending order, the values are mean, median, mode.

Find the mean of the following data set:

\(\displaystyle 33,67,87,23,45,55,136,67,93\)

To find the mean, add up all the terms and divide by the total number of terms.

We have 9 terms, so our denominator will be 9.

\(\displaystyle \frac{33+67+87+23+45+55+136+67+93}{9}=\frac{606}{9}=67.3\bar{3}\approx67.33\)

So our mean is 67.33

The mode of a data set is the data point(s) that appear the most often.

In the data set for this problem, both 4 and 5 appear twice, and no other number appears more than twice.

\(\displaystyle ({2,9,{\color{Blue} 4},{\color{Green} 5},8,3,{\color{Green} 5},{\color{Blue} 4}})\)

So for this data set there are two modes, 4 and 5.

The mean is the average of all the number in the data set.

\(\displaystyle \frac{14+8+23+51}{4} = \frac{96}{4}\)

The answer is:  \(\displaystyle 24\)

The mean is the average of all the numbers given.

Add all the numbers and divide the total by five.

\(\displaystyle \frac{9+5+10+15+21}{5} = \frac{60}{5} = 12\)

The answer is:  \(\displaystyle 12\)

The mean is the average of all numbers in the data set.

Add the numbers, and divide the total sum by four, since there are four numbers.

\(\displaystyle \frac{13+5+8+(-6)}{4} = \frac{20}{4} =5\)

The answer is:  \(\displaystyle 5\)

The mean is the average of the numbers provided.

Sum the numbers and divide the sum by three.

\(\displaystyle \frac{6+9+15}{3} = \frac{30}{3} = 10\)

The answer is:  \(\displaystyle 10\)

Find the median of the following data set:

\(\displaystyle 33,67,87,23,45,55,136,67,93\)

First, put the numbers in ascending order:

\(\displaystyle 23,33,45,55,67,67,87,93,136\)

Next, identify the median by identifying the middle term.

\(\displaystyle 23,33,45,55,{\color{DarkRed} 67},67,87,93,136\)

So, our median is 67.

Order the numbers from least to greatest.

\(\displaystyle [5,-6,17,2] \to [-6,2,5,17]\)

The median of a even set of numbers is the average of the central two numbers.

\(\displaystyle \frac{2+5}{2} = \frac{7}{2}\)

The answer is:  \(\displaystyle \frac{7}{2}\)

The numbers provided are already in chronological order.

Since we have an even set of numbers, the median of the numbers is the average of the two central numbers.

\(\displaystyle \frac{10+11}{2} = \frac{21}{2}\)

Do not confuse the meaning of mean and median!

The answer is:  \(\displaystyle \frac{21}{2}\)