Representing & interpreting data
The idea
Numbers you collect from the real world — heights of plants, votes for a class pet, hours of sleep — are called data, and a messy list of them hides more than it shows. Putting data into a picture makes the story jump out. A tally chart counts in groups of five, a bar graph compares categories with bar heights, and a line plot stacks an X above a number line for every single measurement.
When you read a line plot, remember what one X is: one real plant, one real vote, one real measurement. Reading the plot means counting and comparing Xs — totals, gaps, and clusters. The slippery spot is the tallest stack. A tall tower of Xs above the number 5 does not mean those plants are the tallest; it means 5 was the most common measurement. Height of a stack shows how often a value happened, while the position along the number line shows how big the value is. Keep those two directions straight and line plots become easy.
Worked example
A class measures 9 bean plants to the nearest inch and makes a line plot: 3 plants are 4 inches tall, 4 plants are 5 inches tall, and 2 plants are 6 inches tall. How much taller is the tallest plant than the shortest, and how many plants are at least 5 inches tall?
- Each X on the plot stands for one plant, stacked above its height. Count all the Xs first: 3 + 4 + 2 = 9, matching the 9 plants, so no measurement is missing.
- The smallest height with an X above it is 4 inches and the largest is 6 inches. The gap between tallest and shortest is 6 − 4 = 2 inches.
- For plants at least 5 inches tall, count the Xs above 5 and above 6: 4 + 2 = 6 plants.
- Notice the tallest stack sits above 5 inches. That tells you 5 inches was the most common height — not that those plants are the tallest ones in the group.
Answer. The tallest plant beats the shortest by 2 inches, and 6 of the 9 plants are at least 5 inches tall.
Check your understanding
- What can a line plot show you at a glance that a plain list of the same numbers hides?
- Why does the tallest stack of Xs point to the most common value rather than the biggest value?
- How would the plot change if one more plant grew to 6 inches, and what new comparisons could you make?
- What question would you like to survey your class about, and which kind of display would fit the answers best?