MYP Standard Mathematics Describing and Quantifying Data Notes

Why We Describe And Quantify Data

1. When you collect data from a class survey, a science experiment, or a sustainability study (for example, energy use in different homes), the raw list of values is rarely useful on its own.
2. Describing and quantifying data means turning those values into clear summaries and representations so you can spot relationships, trends, and unusual results.
3. Two big ideas run through this topic:
   1. Where the data tends to be (typical values), and
   2. How spread out the data is (variation).

Data Type Determines What You Can Calculate And Draw

Before calculating any statistics, identify the type of data, because this affects which summaries and graphs are appropriate.

Quantitative data can be split into:

Organizing Raw Data So Patterns Become Visible

Frequency Tables And Grouped Frequency Tables

1. A frequency table records how often each value (or category) occurs.
2. For discrete quantitative or qualitative data, you can usually list each value/category.
3. For continuous data, or when there are many possible values, you often use grouped data, where values are placed into class intervals (for example, 150 to <160 cm).

Stem-And-Leaf Diagrams Preserve Individual Values

1. A stem-and-leaf diagram is a neat way to organize numerical data while still showing every value.
   1. The stem represents the leading digit(s).
   2. The leaf represents the final digit(s).
   3. A key explains how to read the numbers.
2. This makes it easy to see the shape of the distribution and quickly identify the median and quartiles.

Measures Of Central Tendency Describe A Typical Value

The three most common measures are mean, median, and mode.

Mean

1. The mean is the arithmetic average.
2. For ungrouped data with $n$ values $x1, x2, \dots, x_n$: $$\bar{x}=\frac{x1+x2+\cdots+x_n}{n}$$