Investigation 5: Displaying Data

New Concept

We can describe numerical data using statistical measures that summarize key features of a dataset. When describing numerical data, we often use terms such as mean, median, mode, and range which are defined below.

• Mean: The average of the numbers.
• Median: The middle number when the data are arranged in numerical order.
• Mode: The most frequently occurring number.
• Range: The difference between the greatest and least of the numbers.

What’s next

This lesson provides a foundation for data analysis. Next, you’ll tackle worked examples on creating and comparing various graphs and calculating these key statistical measures.

Property

In a pictograph, pictured objects represent the data being counted. Each object represents a certain number of units of data, as indicated in the key.

Examples

If 🍎 = 10 apples, then 🍎🍎🍎 represents 30 apples sold.
If ⭐ = 5 student votes, then ⭐⭐⭐⭐ shows a total of 20 votes for a candidate.
If 🚙 = 1,000,000 cars, then 🚙🚙🚙🚙 shows Michigan produced 4,000,000 cars.

Explanation

Imagine telling a story with pictures instead of words! A pictograph uses cool symbols, like cars or apples, to show amounts. You just check the key to see what each picture is worth and then count them up. It’s a super visual and fun way to compare different groups at a glance.

Property

In a circle graph, each category corresponds to a sector of the circle. The number of degrees in a fraction of a circle is the fraction times $360^\circ$.

Examples

To find the angle for a category representing $\frac{3}{12}$ of the data: $\frac{3}{12} \times 360^\circ = 90^\circ$.
To find the angle for a category representing $\frac{5}{12}$ of the data: $\frac{5}{12} \times 360^\circ = 150^\circ$.
If 25% of students prefer blue, their sector angle is $0.25 \times 360^\circ = 90^\circ$.

Explanation

Think of a pizza! A circle graph, or pie chart, shows parts of a whole, just like slices of a pizza. To figure out how big each slice (sector) should be, you turn its fraction into an angle. Since a full circle is $360^\circ$, a category that's $\frac{1}{4}$ of the total gets a $90^\circ$ slice.

Property

Mean is the average of the numbers. Median is the middle number when data are in order. Mode is the most frequent number. Range is the difference between the greatest and least numbers.

Examples

For data $2, 5, 5, 6, 7$, the Mean (average) is $\frac{2+5+5+6+7}{5} = 5$.
For data $2, 5, 5, 6, 7$, the Median (middle) is $5$ and the Mode (most frequent) is also $5$.
For data $2, 5, 5, 6, 7$, the Range (difference) is the highest minus the lowest: $7 - 2 = 5$.

Explanation

These four terms are like detectives for your data! The mean is the fair share average. The median is the true middle-man when you line everyone up. The mode is the most popular kid in class (the one you see most often). And the range tells you how spread out everything is, from top to bottom.