RWM101: Foundations of Real World Math

8a. Determine the mean, medium, mode, and range from a given set of data

• What is the mean?
• How do you find the mean?
• What is the median?
• How do you find the median?
• What is the mode?
• How do you find the mode?
• What is the range?
• How do you find the range?

For this section, all examples will use the following data set: 3, 4, 5, 5, 7, 10, 13, 14, 15. The numbers in your set are called elements.

The mean is more commonly called "the average". To find the mean, add all of the numbers in your data set, then divide by the number of elements in the set. For example, the sum of the elements in our sample data set is 76. Since there are 9 elements, we divide the sum by 9, making the mean 8.44. $\frac{3+4+5+5+7+10+13+14+15}{9}=8.44$

The median is the "middle number" in the set, when you order the elements from least to greatest. To find the median, first arrange your data set from least to greatest, as in our sample. Then, cross off the numbers one at a time until you find the middle number. Since our data set has 9 elements, the 5th number is the median, which is 7. If your data set has an even number of elements, there isn't 1 middle number, so we find the 2 middle numbers and the mean of those two numbers is the median.

The mode is the element that appears the most number of times in a set. In our example, 5 is the mode, because there are two 5s, and every other element appears once. More than one number can be the mode if 2 or more elements appear the same number of times, but more than any other elements.

The range is the difference between the largest and smallest element in a set. To find the range, subtract the smallest element from the largest. In our example, the range would be 15 - 3 = 12.

To review, see Averages and Probability.

8b. Represent and interpret data in a stem-and-leaf plot

• How do you read a stem-and-leaf plot?
• How does a stem-and-leaf plot help you interpret data?

A stem-and-leaf plot is one way of representing a set of data. Each data point is broken into two parts, the stem and the leaf. The stems are to the left of the vertical line, and the leaves are on the right. Each stem-and- leaf plot has a key that explains how each stem and leaf should be interpreted.

For example:

In the stem-and-leaf plot above, the key shows that the stem is the tens digit, and the leaf is the ones. That means the data in the above set is 7, 11, 14, 18, 25, 25, 25, 26, 27, 27, 29.

A stem-and-leaf plot is an easy way to visualize the spread of the data, and see where the data is concentrated, particularly in a large set of data.

To review, see Stem-and-Leaf Plots.

8c. Represent and interpret data in a line graph

• What is a line graph?
• How do you interpret a line graph?

A line graph is a way of representing data as points above the number line. You use one dot for each corresponding data point. This gives an easy way to view both the values in the data and the spread of the data. For example, consider a data set of 15, 15, 16, 16, 17, 17, 19, 20. The corresponding line graph would be:

Line graphs can also be drawn with a vertical axis, where instead of putting multiple dots vertically to represent the quantity of a single data point, the vertical axis can represent the quantities, and a single dot can be placed to correspond with the quantity of data.

For example:

In the above line graph, you can see that the price is represented on the vertical axis, and then a point is placed to correspond with the correct value for each month.

To review, see Reading Line Graphs.

8d. Represent and interpret data in a bar graph

• What is a bar graph?
• How do you interpret a bar graph?

A bar graph is a graph where categories of data appear on the horizontal axis, and the quantity appears on the vertical axis. For each category, you draw a bar vertically with the height corresponding with the quantity for that category.

In this example, you can see the four teams represented on the horizontal axis, and the bar above each represents the points they scored. The data can be read as approximately Team 1=24, Team 2=36, Team 3=12, and Team 4=38.

To review, see Reading Bar Graphs.

8e. Represent and interpret data in a box-and-whisker plot

• What is a box-and-whisker plot?
• How do I interpret a box-and-whisker plot?

A box-and-whisker plot is an excellent way of representing a lot of data in a way that can clearly show the spread of the data. The spread of the data refers to how much of the data is grouped where. For example, two sets of data could have the same minimum and maximum value, but one set could have many values close to the minimum, while the other may have many values close to the maximum. This can be easily deciphered through a box-and-whisker plot.

In the box-and-whisker plot above, the thin lines extending outward are called the whiskers. The end of the left whisker is the smallest value, called the minimum, and the end of the right whisker is the largest value, the maximum. The line inside the box represents the median, and the ends of the box represent the median of the lower half of the data, also called Quartile 1, and the median of the upper half of the data, also called Quartile 3. In the example above, the minimum would be 41, Quartile 1 is 43, the median is 45, Quartile 3 is 48, and the maximum is 50.

To review, see Box-and-Whisker Plots.

8f. Represent and interpret data in a circle graph

• What is a circle graph?
• How do you interpret a circle graph?

A circle graph, also called a pie graph, is a graph that is a circle broken into sections representing the proportional parts of a whole.

For example:

In this example, you can see that four teams are playing against each other. The relative frequency of how often they win is their percentage, and the size of their section is relative to the percentage. The largest section represents the most wins.

To review, see Reading Pie Graphs (Circle Graphs).

8g. Represent and interpret data in a pictograph

• What is a pictograph?
• How do you interpret a pictograph?

A pictograph is a graph similar to a bar graph, but where the quantity in each category is represented by pictures, rather than the height of a bar. There is usually a key, which tells you how many people/items are represented by each picture. For example:

In this pictograph, each pony image represents 3 ponies, and therefore the Fancy Farm has 15 ponies, Pony Pasture has 6, etc.

To review, see Reading Pictographs.

Unit 8 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

• bar graph
• box-and-whisker plot
• circle graph
• elements
• horizontal axis
• key
• leaf
• line graph
• maximum
• mean
• median
• minimum
• mode
• pictograph
• Quartile 1
• Quartile 3
• range
• spread
• stem
• stem-and-leaf plot
• vertical axis