Data Displays

Dot Plots (Line Plots)

Each dot represents one data value placed above a number line.

Best for: Small data sets, seeing individual values, identifying clusters and gaps.

Histograms

Bars show the frequency of data in intervals (bins).

How to make a histogram:

1. Choose equal-width intervals
2. Count values in each interval (frequency)
3. Draw bars (no gaps between bars!)

Reading histograms: The height shows how many values fall in each interval.

Best for: Large data sets, seeing the shape of a distribution.

Box Plots (Box-and-Whisker Plots)

A box plot shows the five-number summary:

1. Minimum (smallest value)
2. Q1 (first quartile — 25th percentile)
3. Median (middle — 50th percentile)
4. Q3 (third quartile — 75th percentile)
5. Maximum (largest value)

The box spans from Q1 to Q3. The whiskers extend to the min and max.

IQR (Interquartile Range)

$IQR = Q_3 - Q_1$

The IQR measures the spread of the middle 50% of the data.

Choosing the Right Display

| Display | Use When | |---------|----------| | Dot plot | Small data set, see individual values | | Histogram | Large data set, see distribution shape | | Box plot | Compare distributions, see spread | | Bar graph | Categorical data | | Circle graph | Parts of a whole |

Describing Distributions

Use shape, center, and spread:

• Shape: symmetric, skewed left, skewed right
• Center: mean or median
• Spread: range or IQR

Remember: Histograms have no gaps between bars (quantitative data). Bar graphs do have gaps (categorical data).