Do you understand histograms? Did you know that histograms can be a useful way of explaining data?
Jessie works at an ice cream stand. For one hour she recorded the ages of the children who came with their parents to buy ice cream. The histogram above shows this information. Looking at the histogram, can you determine how many persons of each age came to the ice cream stand?
Pay attention and you will know how to answer this question by the end of the Concept.
To understand what a frequency table is, let’s first look at the words themselves. The word frequency refers to how often something occurs. A table is a way of organizing information using columns. Therefore, a frequency table is way of summarizing data by depicting the number of times a data value occurs. To show this, a frequency table organizes the information into a table with three separate columns.
How do we create a frequency table?
First, you need to make a table with three separate columns.
One column is designated for intervals. The number of intervals is determined by the range of data values. Intervals are equal in size and do not overlap. If the range in data values is close together, then the intervals will be small. If the range in data values is spread apart, then the intervals will be larger. It is important that the range of values in each interval is equal and that the values do not overlap from one interval to the next.
Another column is created for tallied results. This is where you tally the number of times you see a data value from each interval. This is where you will see tally marks or lines that record the number of times a data value occurs.
In the last column, add the tally marks to determine the frequency results.
Let’s look at creating a frequency table. Create a frequency table to display the data below.
Step 1: Make a table with three separate columns.
Since the range in data values is not that great, intervals will be in groups of five.
Step 2: Looking at the data, tally the number of times a data value occurs.
Step 3: Add the tally marks to record the frequency.
Take a few minutes to write down the steps for creating a frequency table.
Thinking about the frequency that an event occurs can help you to understand and predict certain trends. Think about how useful the trend of grades could be if you were a teacher thinking about a student’s progress.
We can also create a histogram to display data. Histograms and bar graphs are often confused, but they are different. Let’s look at how.
Ahistogramshows the frequency of data values on a graph. Like a frequency table, data is grouped in intervals of equal size that do not overlap. Like a bar graph, the height of each bar depicts the frequency of the data values. However, on a histogram the vertical columns have no space in between each other.
Create a histogram to display the information on the frequency table.
Here are the steps for creating a histogram from data organized in a frequency table.
Step 1: Draw the horizontal (x) and vertical (y) axis.
Step 2: Give the graph the title “Frequency Table Data.”
Step 3: Label the horizontal axis “Hours.” List the intervals across the horizontal axis.
Step 4: Label the vertical axis “Frequency.” Since the range in frequencies is not that great, label the axis by ones.
Step 5: For each interval on the horizontal access, draw a vertical column to the appropriate frequency value. On a histogram, there is no space in between vertical columns.
Looking at the histogram, you can see that data values between thirty-six and forty were most frequent. Data values between forty-one and forty-five and forty-six and fifty occurred an equal number of times.
Use this histogram of scores earned on math exam to answer the following questions.
Where did the majority of the scores fall?
Solution: Between eighty-six and ninety- five percent
What fraction of the students earned between seventy-six and eighty-five percent?
Which scores were in the minority?
Solution: Between ninety-six and one hundred and five percent
Now back to the dilemma from the beginning of the Concept. Here is the histogram once again.
Let's use it to answer these questions.
What was the most popular age group at the ice cream stand?
There were seven, seven year old children.
How many one year old children came?
How many eight year old children came?
How many ten year old children came?
Notice that you could write many questions and answers using this histogram. The histogram provides a wonderful visual display of the data.
information that has been collected regarding an occurrence or an event.
a graph that uses columns to compare quantities or amounts.
a display that summarizes data by depicting the number of times that a data value occurs.
a display that shows the frequency of data values on a graph.
Here is one for you to try on your own.
The data values below depict student scores (out of 100%) on a recent math exam. Organize the data into a frequency table.