Interpret histograms

key notes :

1. Understanding Histograms

  • A histogram is a type of bar graph that represents the distribution of numerical data by showing the frequency of data points within specified intervals (bins).
  • Unlike bar graphs, histograms display data that is continuous, meaning the bars touch each other.

2. Parts of a Histogram

  • Title: Describes what the histogram represents.
  • X-axis (Horizontal axis): Represents the intervals or bins of data, showing the range of values grouped together.
  • Y-axis (Vertical axis): Represents the frequency or count of data points within each interval.
  • Bars: Each bar represents the frequency of data points within a specific interval. The height of the bar corresponds to how many data points fall within that interval.

3. Steps to Interpret a Histogram

  • Step 1: Read the Title: Understand what the histogram is about.
  • Step 2: Analyze the X-axis: Look at the intervals to understand the range of data being represented.
  • Step 3: Analyze the Y-axis: Check the scale to understand the frequency of data points.
  • Step 4: Examine the Bars: The height of each bar indicates how many data points fall within the corresponding interval.
  • Step 5: Draw Conclusions: Use the histogram to identify patterns, such as which interval has the most or least data points.

4. Identifying Key Features in Histograms

  • Peak (Mode): The tallest bar represents the interval with the highest frequency, also known as the mode.
  • Spread: Look at how wide the data is spread across the intervals. This shows the range of the data.
  • Skewness:
    • Left-skewed (negative skew): Most data points are concentrated on the right side.
    • Right-skewed (positive skew): Most data points are concentrated on the left side.
    • Symmetrical: Data is evenly distributed on both sides of the peak.

5. Comparing Histograms

  • Compare different histograms by looking at the spread, peak, and skewness to understand how the distributions differ.
  • Compare the height of bars in different histograms to see which data set has more frequent values within certain intervals.

6. Common Mistakes to Avoid

  • Misinterpreting the intervals: Remember that each bar represents the frequency of data within a specific interval, not individual values.
  • Confusing histograms with bar graphs: Unlike bar graphs, the bars in histograms touch because the data is continuous.

7. Applications of Histograms

  • Histograms are often used in statistics to display the distribution of data points, such as test scores, temperatures, or any other quantitative data.
  • They help in identifying the central tendency, spread, and overall shape of the data distribution.

Learn with an example

🔔 The staff of a game show tracked the performance of all the contestants during the past season.

Which score range was achieved by the most people?

  • 1-5 points
  • 6-10 points
  • 21-25 points
  • 31-35 points

Find the tallest bar. The tallest bar is for the range 1-5.

The score range 1-5 was achieved by the most people.

🔔 Dr. Baldwin, a paediatrician, weighed all the children who recently visited her office.

How many children weighed between 11 and 20 pounds?

  _________children

Find the bar for the range 11-20. Using the scale on the left side of the graph, read the height of the bar. The height of the bar is 1.

1 child weighed between 11 and 20 pounds.

🔔While hanging Christmas lights for neighbours, Lorenzo counted the number of broken lights on each string.

Which range of broken lights per string occurred least frequently?

  • 1- 5 broken lights
  • 11- 15 broken lights
  • 21- 25 broken lights
  • 26-30 broken lights

Find the shortest bar. The shortest bar is for the range 11-15.

The range 11-15 occurred least frequently.

Let’s practice!🖊️