Reading and Creating Histograms

A histogram is a special type of graph used to display continuous data. Instead of showing individual data points, a histogram groups data into equal-width ranges, often called bins or intervals, and uses bars to show the frequency (how many data points) in each bin.

Histograms vs. Bar Graphs

While they look similar, histograms and bar graphs are used for different types of data:

• Bar Graphs are used for categorical data (like favorite colors or types of pets). The bars usually have gaps between them.
• Histograms are used for continuous numerical data (like heights, ages, or test scores). Because the numbers flow continuously from one interval to the next, the bars in a histogram always touch.

Creating a Histogram

Let's create a histogram using this set of test scores: $65, 71, 78, 79, 82, 85, 88, 89, 91, 95$

Step 1: Choose equal-width intervals (bins). Let's use intervals of $10$ for our data: $60-69$, $70-79$, $80-89$, and $90-99$.

Step 2: Count the frequency for each bin. Make a frequency table to count how many scores fall into each range:

• $60-69$: $1$ (the score $65$)
• $70-79$: $3$ ($71, 78, 79$)
• $80-89$: $4$ ($82, 85, 88, 89$)
• $90-99$: $2$ ($91, 95$)

Step 3: Draw and label your axes.

• The x-axis (bottom) represents the intervals ($60-69$, $70-79$, etc.).
• The y-axis (side) represents the frequency (from $0$ to at least $4$).

Step 4: Draw the bars. Draw a bar for each interval up to its corresponding frequency. Remember, make sure the edges of the bars touch!

Reading a Histogram

When looking at a histogram, you can quickly answer questions about the data's distribution by looking at the height of the bars.

Example Question: Looking at the data we just grouped, how many students scored in the $80-89$ range? Answer: You would locate the $80-89$ bin on the x-axis and look at the height of that bar on the y-axis. The height is $4$, so $4$ students scored in that range.

Example Question: How many total students took the test? Answer: Add the heights of all the bars together: $1 + 3 + 4 + 2 = 10$ students.