MYP Standard Mathematics Histograms Notes

Why Histograms Matter For Quantitative Data

1. Histograms are one of the most useful ways to see the shape of a data set at a glance.
2. They are designed for quantitative data (numerical values) and are especially important when the data are continuous (measured values like mass, height, time, and temperature), where values can take any number within an interval.
3. In MYP Standard Mathematics, histograms support three core skills:
   1. Constructing bar charts and histograms correctly
   2. Interpreting frequency and relative frequency histograms
   3. Visualizing key characteristics of a distribution (where the data cluster, how spread out they are, and whether the data are skewed)

Bar Charts And Histograms Look Similar, But Represent Different Data

1. Both displays use rectangular bars, but they answer different questions.
2. Confusing them is one of the most common causes of incorrect graphs and incorrect interpretation.

Bar Charts Summarize Categories

1. A bar chart represents qualitative (categorical) data, such as type of fruit, eye color, or favorite sport.
2. Key features:
   1. Bars have equal width.
   2. There are spaces between bars because categories are separate.
   3. The height of the bar represents the frequency.
   4. The vertical axis is typically labeled frequency.

Histograms Summarize Numerical Values

1. A histogram represents quantitative data, including all continuous data and sometimes discrete numerical data (when it is appropriate to group the values).
2. Key features:
   1. Each bar represents a class interval (a numerical range).
   2. Bars touch because the intervals connect with no gaps.
   3. The area of each bar represents the frequency.
   4. The vertical axis may show frequency, relative frequency, or frequency density.