Data Displays

📊 Data Displays

Part 1 of 5 — Dot Plots & Frequency Tables

Topics in This Part

🔑 Key Concept: A data display is a picture of numbers. The whole point is to take a messy list of values and arrange it so you can see the story — which values are common, which are rare, and how spread out everything is.

What Counts as Data?

Data is just a collection of facts you gather, usually numbers. When you ask a question like "How many pets does each student have?" and write down the answers, that list of answers is your data.

Suppose you asked 12 classmates how many pets they own and got:

$2,\; 0,\; 1,\; 3,\; 2,\; 1,\; 0,\; 2,\; 4,\; 1,\; 2,\; 0$

That raw list is hard to read. Two questions are tricky to answer just by staring at it:

• How many students own exactly 2 pets?
• What is the most common number of pets?

To answer those quickly, we organize the data. The first tool is a frequency table.

💡 Frequency is a fancy word for how many times something happens. If three students own 2 pets, the frequency of "2 pets" is 3.

Count From the Raw List 🔽

Look back at the raw pet list: $2,\; 0,\; 1,\; 3,\; 2,\; 1,\; 0,\; 2,\; 4,\; 1,\; 2,\; 0$. Count carefully.

Frequency Tables

A frequency table lists each value once and counts how many times it appears. Here is the pet data organized:

Now the data tells its story instantly:

• 4 students own 2 pets — that's the most common value.
• The frequencies add up to $3 + 3 + 4 + 1 + 1 = 12$, which matches our 12 classmates. ✓

Concept Check 🎯

Dot Plots (Line Plots)

A dot plot (also called a line plot) shows the same information as a frequency table, but with a stack of dots above each value on a number line. One dot = one data point.

Here is the pet data as a dot plot:

            ●
●     ●     ●
●     ●     ●
●     ●     ●     ●     ●
0     1     2     3     4
   Number of pets

Reading it is easy:

• Count the dots in a column to get that value's frequency.
• The tallest stack is the most common value (here, 2 pets with 4 dots).
• A gap (a value with no dots) means nobody had that amount.

💡 Dot plots shine for small data sets of whole numbers. You can see the shape — where data clumps up and where it thins out — at a single glance.

Read the Dot Plot 🧮

A class recorded how many books each student read last month:

            ●
●           ●     ●
●     ●     ●     ●
●     ●     ●     ●     ●
1     2     3     4     5
     Number of books

1) How many students read exactly 3 books? 2) How many students read 5 books? 3) How many students are in the class in total?

Wrapping Up Part 1

You now have two ways to organize a list of numbers:

Both answer the same questions — what's common, what's rare, how many total — they just look different.

In Part 2 we'll handle data with lots of different values using bar graphs and histograms.

📊 Data Displays

Part 2 of 5 — Bar Graphs & Histograms

🔑 The Big Difference: A bar graph compares separate categories (like favorite colors). A histogram groups numbers into ranges called bins (like test scores 70–79, 80–89). They look similar, but one is for categories and the other is for number ranges.

Bar Graphs

A bar graph uses bars to compare categories. The height (or length) of each bar shows the frequency for that category. Because the categories are separate things, the bars have gaps between them.

Students voted for their favorite school lunch:

Votes
 9 |  █
 6 |  █     █
 3 |  █     █           █
 0 |  █     █     █     █
      Pizza Tacos Salad Pasta

To read a bar graph, line the top of each bar up with the scale on the left.

💡 Categories can be put in any order on a bar graph. Pizza first or pasta first — it doesn't change the data, because the categories aren't numbers on a line.

Concept Check 🎯

📊 Data Displays

Part 3 of 5 — Stem-and-Leaf Plots & Line Graphs

🔑 Why these two? A stem-and-leaf plot keeps every exact value while still showing the shape of the data. A line graph shows how one thing changes over time. Each is the right tool for a different job.

Stem-and-Leaf Plots

A stem-and-leaf plot splits each number into a stem (the left digits) and a leaf (the last digit). For two-digit numbers, the tens digit is the stem and the ones digit is the leaf.

Here are 11 quiz scores:

$62,\; 75,\; 78,\; 81,\; 83,\; 83,\; 90,\; 71,\; 88,\; 95,\; 79$

📊 Data Displays

Part 4 of 5 — Shape, Center & Spread

🔑 Reading the Story: Every display has a shape. By looking at where the data clumps and how it stretches out, you can describe its center (a typical value), its spread (how far apart the values are), and any outliers (values far from the rest).

The Shape of Data

Look at a dot plot or histogram from across the room and notice its shape.

A cluster is where data bunches together. A gap is a range with no data. An outlier is a single value sitting far away from everything else.

●
●  ●
●  ●  ●              ●   ← outlier (far from the cluster)
1  2  3  4  5  6  7  8

📊 Data Displays

Part 5 of 5 — Choosing Displays & Mastery Check

You can now build and read dot plots, frequency tables, bar graphs, histograms, stem-and-leaf plots, and line graphs — and describe a data set's shape, center, and spread. The last skill is choosing the right display and reading displays critically.

Choosing the Right Display

🔑 The key question is always: What kind of data is it, and what do I want to show? Categories vs. numbers, and "over time" vs. "all at once," decide nearly every choice.

Concept Check 🎯

Reading Displays Critically