Mathematics
Grade 6
15 min
Interpret histograms
Interpret histograms
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1
Introduction & Learning Objectives
Learning Objectives
Identify the key components of a histogram, including axes, intervals, and frequency.
Determine the frequency of data within a specific interval from a given histogram.
Compare frequencies across different intervals in a histogram.
Describe the general shape or distribution of data presented in a histogram.
Answer questions about a dataset by interpreting its histogram.
Distinguish between a histogram and a bar graph based on their characteristics.
Have you ever wondered how to quickly see patterns in a lot of numbers, like test scores or daily temperatures? 📊 Histograms are like special picture stories that help us do just that!
In this lesson, you'll learn how to read and understand histograms. These powerful graphs help us make sense of large am...
2
Key Concepts & Vocabulary
TermDefinitionExample
HistogramA type of bar graph that shows how often data falls into certain ranges or intervals. The bars touch each other to show continuous data.A histogram showing the number of students who scored between 0-10, 11-20, 21-30, etc., on a math test.
Interval (or Bin)A range of values on the horizontal (x) axis that each bar in a histogram represents. These ranges are usually equal in size.In a histogram of test scores, an interval might be '71-80', meaning all scores from 71 up to and including 80.
FrequencyThe number of times a data value occurs within a specific interval. It is shown by the height of each bar on the vertical (y) axis.If a bar for the '71-80' interval reaches a height of 5, it means 5 students scored between 71 and 80.
X-axis (Hor...
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Core Formulas
Rule 1: Read the Axes Labels and Scales
Always start by looking at what the X-axis (horizontal) and Y-axis (vertical) represent and what their scales are. The X-axis shows the data intervals, and the Y-axis shows the frequency.
This helps you understand what data is being displayed and how to measure the frequency. For example, if the X-axis is 'Age (years)' and the Y-axis is 'Number of People', you know you're looking at how many people are in different age groups.
Rule 2: Understand Intervals on the X-axis
Each bar on a histogram represents a range of values (an interval) on the X-axis, not a single value. The bars usually touch to show that the data is continuous.
When you see a bar, remember it covers all the numbers within that specific range. F...
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Challenging
A histogram shows the daily screen time for 60 students. The intervals are 0-59 min (12 students), 60-119 min (24 students), 120-179 min (15 students), and 180+ min (9 students). A new school rule states that students with 2 hours or more of screen time must attend a workshop. What percentage of students must attend?
A.25%
B.15%
C.60%
D.40%
Challenging
Two histograms are presented. Histogram A shows test scores for a class that studied for an exam. It has a tall bar in the 80-100 range. Histogram B shows scores for a class that did not study. It has a tall bar in the 50-70 range. Which is the most reasonable conclusion?
A.Both classes performed equally well.
B.The class that studied (Histogram A) generally scored higher than the class that did not (Histogram B).
C.The class that did not study (Histogram B) had a few students who scored very high.
D.The total number of students in both classes is the same.
Challenging
A histogram shows the heights of 100 trees. The shape of the histogram is roughly symmetrical, like a bell, with the tallest bar at the '20-24 feet' interval. What can you most likely infer about the average height of a tree in this group?
A.The average height is likely to be within the 20-24 feet interval.
B.The average height is likely to be very low, around 0-4 feet.
C.The average height is likely to be very high, over 40 feet.
D.It's impossible to infer anything about the average from the shape.
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